L'attività di ricerca di chi scrive si è finora indirizzata principalmente verso l'esame dei modelli di transizione di fase, dei modelli di isteresi, e delle relative equazioni non lineari alle derivate parziali. Qui si illustrano brevemente tali problematiche, indicando alcuni degli elementi che le collegano tra di loro. Il lavoro è organizzato come segue. I paragrafi 1, 2, 3 vertono sulle transizioni di fase: si introducono le formulazioni forte e debole del classico modello di Stefan, e si illustrano alcune generalizzazioni motivate fisicamente. Nei paragrafi 4, 5, 6 si definisce il concetto di operatore di isteresi, si forniscono alcuni esempi, e si discutono alcune equazioni alle derivate parziali in cui figurano tali operatori. Le due parti sono presentate in modo da consentirne una lettura indipendente.
@article{BUMI_2000_8_3B_1_31_0, author = {Augusto Visintin}, title = {Transizioni di fase ed isteresi}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {3-A}, year = {2000}, pages = {31-77}, zbl = {1064.74139}, mrnumber = {1755701}, language = {it}, url = {http://dml.mathdoc.fr/item/BUMI_2000_8_3B_1_31_0} }
Visintin, Augusto. Transizioni di fase ed isteresi. Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000) pp. 31-77. http://gdmltest.u-ga.fr/item/BUMI_2000_8_3B_1_31_0/
[1]
, Homogeneous Nucleation Theory, Academic Press, New York1974.[2]
, The Growth of Crystals from Liquids, North-Holland, Amsterdam1973.[3]
, Principles of Solidification, Wiley, New York1964.[4]
, The Theory of Transformations in Metals and Alloys. Part 1: Equilibrium and General Kinetic Theory, Pergamon Press, London1975.[5]
, Rates of Phase Transformations, Academic Press, Orlando1985.[6]
, Solidification Processing, McGraw-Hill, New York1973.[7]
- , Fundamentals of Solidification, Trans Tech, Aedermannsdorf1989.[8]
(ed.), Crystal Growth, Pergamon Press, Oxford 1975.[9]
, Metastable Liquids, Wiley, Chichester1974.[10] Phase Changes, Solid State Physics, 3 (1956), 225-306.
,[11]
, The Molten State of Matter, Wiley, Chichester1978.[12]
, The Solid-Liquid Interface, Cambridge Univ. Press, Cambridge1973.[13]
- , Mathematical Modeling of Melting and Freezing Processes, Hemisphere Publishing, Washington DC1993.[14] | MR 1411908 | Zbl 0951.74002
- , Hysteresis and Phase Transitions, Springer, Heidelberg1996.[15] | MR 1402243 | Zbl 0787.73004
, Thermomechanics of Evolving Phase Boundaries in the Plane, Clarendon Press, Oxford1993.[16] | MR 1154310 | Zbl 0751.35052
, The Stefan Problem, De Gruyter, Berlin1992 (Russian edition: Nauka, Novosibirsk 1986).[17] | MR 1347688 | Zbl 0827.73001
, Thermomechanics of Phase Transitions in Classical Field Theory, World Scientific, Singapore1993.[18] | MR 222436
, The Stefan Problem.A.M.S., Providence1971 (Russian edition: Zvaigzne, Riga 1967).[19] | MR 1423808 | Zbl 0882.35004
, Models of phase transitions, Birkhauser, Boston1996.[20] The One-Dimensional Heat Equation, Encyclopedia of Mathematics and its Applications, Vol. 23, Addison Wesley, Menlo Park1984. | MR 747979 | Zbl 0567.35001
,[21] Macroscopic models for superconductivity, S.I.A.M. Rev., 34 (1992), 529-560. | MR 1193011 | Zbl 0769.73068
- - ,[22] On the Stefan problem, Russian Math. Surveys, 40 (1985), 157-223. | MR 810813 | Zbl 0604.35080
,[23] Las Zonas Pastosas en el Problema de Stefan, Cuad. Inst. Mat. Beppo Levi, No. 13, Rosario1987. | MR 914370 | Zbl 0642.35081
,[24] Esperienza di collaborazione con industrie su programmi a lungo termine, Boll. Un. Matem. Ital., 7-A (1997), 1-40. | Zbl 0973.00517
,[25] Phase transition with supercooling, Boll. Un. Matem. Ital., (8) (1998), 49-69. | MR 1619031 | Zbl 0903.35095
,[26] Problemi di Stefan bifase in piu variabili spaziali, Le Matematiche, 36 (1981), 65-108. | MR 736797 | Zbl 0545.35096
,[27] Stefan problems with a concentrated capacity, Boll. Un. Matem. Ital., (8) (1998), 71-81. | MR 1619035 | Zbl 0904.35103
,[28] Stefan-like problems, In: Free Boundary Problems: Theory and Applications ( , , eds.). Pitman, Boston 1983, pp. 321-347. | MR 714922
,[29] Stefan-like problems, Meccanica, 28 (1993), 129-143. | Zbl 0786.76091
- - ,[30] Problemi a contorno libero per l'equazione della diffusione, Rend. Sem. Mat. Univers. Politecn. Torino, 32 (1973-74), 183-206. | MR 477466 | Zbl 0307.76048
,[31] Problemi di diffusione a frontiera libera, Boll. Un. Matem. Ital., 18-A (1981), 11-68. | Zbl 0468.35082
,[32] The variational inequality approach to the one-phase Stefan problem, Acta Applicandae Mathematicae, 8 (1987), 1-35. | MR 871691 | Zbl 0653.35083
,[33] A Bibliography on Moving-Free Boundary Problems for the Heat Diffusion Equation. The Stefan Problem, Progetto Nazionale M.P.I. «Equazioni di Evoluzione e Applicazioni Fisico-Matematiche», Firenze, 1988. | MR 1007840 | Zbl 0694.35221
,[34] Numerical methods for phase transition problems, Boll. Un. Matem. Ital., (8) (1998), 83-108. | MR 1619039 | Zbl 0896.65064
,[35] Introduction to the models of phase transitions, Bull. Un. Matem. Ital., I-B (1998), 1-47. | MR 1619027 | Zbl 0903.35097
,[36] A Bibliography on Moving Boundary Problems with Key Word Index, Oak Ridge National Laboratory, 1979.
- - ,[37]
- - (EDS.), Free Boundary Problems: Theory and Applications, Pitman, Boston 1985.[38] | MR 1216352
- (EDS.), Emerging Applications in Free Boundary Problems, Longman, Harlow 1993.[39] | MR 1216392
- (eds.), Free Boundary Problems Involving Solids, Longman, Harlow 1993.[40] | MR 1216373
- (eds.), Free Boundary Problems in Fluid Flow with Applications, Longman, Harlow 1993.[41] | MR 1342322
- - , (eds.), Free Boundary Problems: Theory and Applications, Longman, Harlow 1995.[42] | MR 714939 | Zbl 0504.00012
- (eds.), Free Boundary Problems: Theory and Applications, Pitman, Boston 1983.[43] | Zbl 0703.00015
- (eds.), Free Boundary Problems: Theory and Applications, Longman, Harlow 1990.[44] | MR 1111018 | Zbl 0702.00021
- (eds.), Free Boundary Value Problems, Birkhäuser, Boston 1990.[45] | MR 1422923
- - (eds.), Nonlinear Analysis and Applications, Gakkotosho, Tokyo 1996.[46]
(ed.), Free Boundary Problems, Istituto di Alta Matematica, Roma 1980.[47] | MR 1462964 | Zbl 0856.00025
- (EDS.), Free Boundary Problems: Theory and Applications, Longman, Harlow 1996.[48] | Zbl 0295.76064
- (eds.), Moving Boundary Problems in Heat Flow and Diffusion, Clarendon Press, Oxford 1975.[49] | MR 466887 | Zbl 0432.00011
- - (eds.), Moving Boundary Problems, Academic Press, New York 1978.[50] Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems, Ann. Math., 143 (1996), 413-434. | MR 1394964 | Zbl 0853.35049
- - ,[51] Regularity of the free boundary in phase transition problems, Acta Math., 176 (1996). | Zbl 0891.35164
- - ,[52] Phase transition problems of parabolic type: flat free boundaries are smooth, Comm. Pure Appl. Math., 51 (1998), 77-112. | MR 1486632 | Zbl 0924.35197
- - ,[53] Su un problema di frontiera libera connesso a questioni di idraulica, Ann. Mat. Pura Appl., 92 (1972), 107-127. | MR 408443 | Zbl 0258.76069
,[54] | MR 745619 | Zbl 0551.49007
- , Variational and Quasivariational Inequalities, Applications to Free Boundary Problems, Wiley, Chichester1983.[55] A numerical method for solving the problem , R.A.I.R.O., Analyse Numérique, 13 (1979), 297-312. | MR 555381 | Zbl 0426.65052
- - ,[56] Some properties of the nonlinear semigroup for the problem , Nonlinear Analysis, T.M.A., 8 (1984), 909-939. | MR 753767 | Zbl 0557.35129
- ,[57] On some degenerate nonlinear parabolic equations, In: Nonlinear Functional Analysis ( , ed.). Proc. Symp. Pure Math., XVIII A.M.S., Providence 1970, pp. 28-38. | MR 273468 | Zbl 0231.47034
,[58] The regularity of free boundaries in higher dimensions, Acta Math., 139 (1977), 155-184. | MR 454350 | Zbl 0386.35046
,[59] Some aspects of the one-phase Stefan problem, Indiana Univ. Math. J., 27 (1978), 73-77. | MR 466965 | Zbl 0393.35064
,[60] Continuity of the temperature in the two-phase Stefan problem, Arch. Rational Mech. Anal., 81 (1983), 199-220. | MR 683353 | Zbl 0516.35080
- ,[61] Continuity of the temperature in the Stefan problem, Indiana Univ. Math. J., 28 (1979), 53-70. | MR 523623 | Zbl 0406.35032
- ,[62] On the infinite differentiability of the free boundary in a Stefan problem, J. Math. Anal. Appl., 22 (1968), 385-387. | MR 225013 | Zbl 0167.10504
- ,[63] Homogenization for eddy currents, Delft Progress Report, 6 (1981), 268-275. | Zbl 0483.35004
,[64] Regularity results for the n-dimensional two-phase Stefan problem, Boll. Un. Mat. Ital. Suppl. (1980), 129-152. | MR 677695 | Zbl 0458.35098
,[65] Continuity of weak solutions to certain singular parabolic equations, Ann. Mat. Pura Appl., 121 (1982), 131-176. | MR 663969 | Zbl 0503.35018
,[66] On the singular equation , Arch. Rational Mech. Anal., 132 (1995), 247-309. | MR 1365831 | Zbl 0849.35060
- ,[67] A model for non-equilibrium thermodynamic processes involving phase changes, J. Inst. Math. Appl., 24 (1979), 425-438. | MR 556152 | Zbl 0426.35060
,[68] Résolution d'un problème de Stefan (fusion d'un bloc de glace à zéro degrés), C.R. Acad. Sci. Paris, Série I, 276-A (1973), 1461-1463. | MR 328346 | Zbl 0258.35037
,[69] The solution of a two-phase Stefan by a variational inequality, In: Moving Boundary Problems in Heat Flow and Diffusion ( , , eds.), Clarendon Press, Oxford 1975, pp. 173-181.
,[70] A note on the existence of a solution to a Stefan problem, Quart. Appl. Math., IX (1951), 185-193. | Zbl 0043.41101
,[71] General free boundary problems for the heat equation, J. Math. Anal. Appl.: I, 57 (1977), 694-723; II, 58 (1977), 202-231; III, 59 (1977), 1-14. | Zbl 0355.35037
- ,[72] Free boundary problems for nonlinear parabolic equations with nonlinear free boundary conditions, J. Math. Anal. Appl., 72 (1979), 247-273. | MR 552335 | Zbl 0421.35080
- ,[73] Phase-change with volumetric heat sources: Stefan's scheme vs. enthalpy formulation, Boll. Un. Mat. Ital. Suppl., 4 (1985), 131-149. | MR 784301 | Zbl 0578.35087
- ,[74] Mushy regions with variable temperature in melting processes, Boll. Un. Mat. Ital., 4-B (1985), 601-626. | MR 805431 | Zbl 0591.35088
- ,[75] A parabolic-hyperbolic free boundary problem, S.I.A.M. J. Math. Anal., 17 (1986), 67-73. | MR 819213 | Zbl 0594.35092
- ,[76] A critical case for the solvability of Stefan-like problems, Math. Meth. Appl. Sci., 5 (1983), 84-96. | MR 690897 | Zbl 0526.35078
- ,[77] Regularity of weak solutions of one-dimensional two-phase Stefan problems, Ann. Mat. Pura Appl., 115 (1977), 341-348. | MR 477460 | Zbl 0378.35008
- - ,[78] Variational formulation of the Stefan problem, coupled Stefan problem, frost propagation in porous media, In: Proc. Conf. Computational Methods in Nonlinear Mechanics ( , ed.). University of Texas, Austin (1974), pp. 341-349. | MR 398299 | Zbl 0316.76063
,[79] Free boundary problems for parabolic equations. I, II, III, J. Math. Mech., 8 (1959), 499-517; 9 (1960), 19-66; 9 (1960), 327-345. | Zbl 0199.42301
,[80] | MR 181836 | Zbl 0144.34903
, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs1964.[81] The Stefan problem in several space variables, Trans. Amer. Math. Soc., 133 (1968), 51-87. | MR 227625 | Zbl 0162.41903
,[82] One dimensional Stefan problems with non-monotone free boundary, Trans. Amer. Math. Soc., 133 (1968), 89-114. | MR 227626 | Zbl 0162.42001
,[83] Analyticity of the free boundary for the Stefan problem, Arch. Rational Mech. Anal., 61 (1976), 97-125. | MR 407452 | Zbl 0329.35034
,[84] A one phase Stefan problem, Indiana Univ. Math. J., 25 (1975), 1005-1035. | MR 385326 | Zbl 0334.49002
- ,[85] Nonincrease of mushy region in a nonhomogeneous Stefan problem, Quart. Appl. Math., XLIX (1991), 741-746. | MR 1134749 | Zbl 0756.35119
- ,[86] The two-phase Stefan problem. I, II, Chinese Math., 4 (1963), 686-702; 5 (1964), 36-53. | Zbl 0149.31601
,[87] On the Stefan problem, Math. Sbornik, 53 (1961), 489-514 (Russian). | Zbl 0102.09301
,[88] Regularity in free boundary value problems, Ann. Scuola Norm. Sup. Pisa, 4 (1977), 373-391. | MR 440187 | Zbl 0352.35023
- ,[89] The smoothness of the free boundary in the one-phase Stefan problem, Comm. Pure Appl. Math., 31 (1978), 257-282. | MR 480348 | Zbl 0391.35060
- ,[90] Free boundary problem for the heat equation with applications to problems with change of phase, Comm. Pure Appl. Math., 10 (1957), 220-231. | Zbl 0070.43803
,[91] Mémoire sur la solidification par refroidissement d'un globe solide, Ann. Chem. Phys., 47 (1831), 250-256.
, ,[92] Solutions of the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature, Euro. J. Appl. Math., 1 (1990), 101-111. | MR 1117346 | Zbl 0734.35159
,[93] On the classical solvability of the Stefan problem, Soviet Math. Dokl., 20 (1979), 1426-1429. | Zbl 0498.35087
,[94] On the classical solution of the multidimensional Stefan problem for quasilinear parabolic equations, Math. U.S.S.R.-Sbornik, 40 (1981), 157-178. | Zbl 0467.35053
,[95] An example of nonexistence of a classical solution of the Stefan problem, Soviet Math. Dokl., 23 (1981), 564-566. | MR 620870 | Zbl 0545.35097
,[96] A method of solution of the general Stefan problem, Soviet Math. Dokl., 1 (1960), 1350-1353. | MR 125341 | Zbl 0131.09202
,[97] Mushy regions in phase-change problems, In: Applied Functional Analysis ( , , eds.). Lang, Frankfurt (1983), pp. 251-269. | MR 685609 | Zbl 0518.35087
,[98] | MR 1038061 | Zbl 0676.00021
(ed.), Mathematical Models for Phase Change Problems, Birkhäuser, Basel 1989.[99] On the determination of the position of the boundary which separates two phases in the one-dimensional problem of Stefan, Dokl. Acad. Nauk USSR, 58 (1947), 217-220. | MR 22979 | Zbl 0032.13101
,[100] Remarks on the analyticity of the free boundary for the one-dimensional Stefan problem, Ann. Mat. Pura Appl., 125 (1980), 295-311. | MR 605212 | Zbl 0456.35096
- - ,[101] A new proof of infinite differentiability of the free boundary in the Stefan problem, J. Differential Equations, 20 (1976), 266-269. | MR 390499 | Zbl 0314.35044
,[102] Esistenza di una soluzione in problemi analoghi a quello di Stefan, Rivista Mat. Univ. Parma, 3 (1952), 3-23; 8 (1958), 1-209. | Zbl 0048.43406
,[103] Mathematical formulation of the Stefan problem, Int. J. Eng. Sc., 20 (1982), 909-912. | MR 660566 | Zbl 0506.76103
,[104] Über einige Probleme der Theorie der Wärmeleitung, Sitzungber., Wien, Akad. Mat. Natur., 98 (1889), 473-484. Also ibid. pp. 614-634, 965-983, 1418-1442. | JFM 21.1197.01
,[105] Two-scale Stefan problem with surface tension, In: Nonlinear Analysis and Applications ( , , , eds.) (Gakkotosho, Tokyo 1996), 405-424. | MR 1422948 | Zbl 0868.35144
,[106] Two-scale model of phase transitions, Physica D, 106 (1997), 66-80. | MR 1460449 | Zbl 0935.80005
,[107] Nucleation and mean curvature flow, Communications in P.D.E.s, 23 (1998), 17-35. | MR 1608492 | Zbl 0901.53045
,[108] Interior and boundary continuity of weak solutions of degenerate parabolic equations, Trans. A.M.S., 271 (1982), 733-748. | MR 654859 | Zbl 0506.35053
,[109]
, Hysteresis in Magnetism, Academic Press, Boston1998.[110] Optimal control of ordinary differential equations with nonlinearities of hysteresis type. In: Automation and Remote Control, 52 (1991), 53 (1992). | MR 1031251 | Zbl 0691.49025
, Optimale Steuerung von gewöhnlichen Differentialgleichungen mit Nichtlinearitäten vom Hysteresis-Typ, Lang, Frankfurt am Main (1987). English translation:[111] | MR 1411908 | Zbl 0951.74002
- , Hysteresis and Phase Transitions, Springer, Berlin1996[112]
, Magnetic Hysteresis, IEEE Press, 1999.[113]
, Hysteresis Models in Electromagnetic Computation, Akademḿiai Kiado, Budapest, 1997.[114] | MR 987431 | Zbl 0665.47038
- , Systems with Hysteresis, Springer, Berlin1989 (Russian ed. Nauka, Moscow 1983).[115] | Zbl 1187.35003
, Convexity, Hysteresis and Dissipation in Hyperbolic Equations, Gakkotosho, Tokyo1997.[116] | MR 1083150 | Zbl 0723.73003
, Mathematical Models of Hysteresis, Springer, New York1991.[117] | MR 1329094 | Zbl 0820.35004
, Differential Models of Hysteresis, Springer, Berlin1994.[118] Elastoplastic constitutive laws of nonlinear kinematic hardening type, In: Functional analysis with current applications in science, technology and industry ( , , eds.), Longman, Harlow (1998), pp. 238-272. | MR 1607891 | Zbl 0911.73021
,[119] Non-equilibrium thermodynamics of pseudoelasticity, Cont. Mech. Thermodyn., 5 (1993), 163-204. | Zbl 0780.73006
- ,[120] Equations with non-linearities of hysteresis type, VII Int. Konf. Nichtlin. Schwing., Berlin 1975; Abh. Akad. Wiss. DDR, 3 (1977), 437-458 (Russian). | Zbl 0406.93032
,[121] Evolution variational inequalities and multidimensional hysteresis operators, In: Nonlinear differential equations ( , , , eds.) Research Notes in Mathematics, Chapman & Hall/CRC, London (1999), pp. 47-110. | Zbl 0949.47053
,[122] Six lectures on shape memory, Proceedings of a Summer School held in Banff in 1995. AMS. CRM Proceedings and Lecture Notes, 13 (1998), pp. 125-161. | MR 1619114 | Zbl 0909.73013
,[123] Mathematical models for hysteresis, S.I.A.M. Review, 35 (1993), 94-123. | MR 1207799 | Zbl 0771.34018
- - ,[124] Mathematical models of hysteresis, In: Topics in Nonsmooth Mechanics ( , , , eds.), Birkhäuser, Basel 1988, pp. 295-326. | MR 957094 | Zbl 0656.73043
,[125] Mathematical models of hysteresis, In: Modelling and optimization of distributed parameter systems ( et al., ed.), Chapman and Hall, (1996), pp. 71-80 | MR 1388519 | Zbl 0906.93006
,[126] Mathematical models of hysteresis. A survey, In: Nonlinear Partial Differential Equations. College de France. Vol. XIII ( , , eds.), Longman, Harlow (1998), pp. 327-338. | MR 1773088 | Zbl 1007.47034
,[127] Six talks on hysteresis, Proceedings of a Summer School held in Banff in 1995. AMS. CRM Proceedings and Lecture Notes, 13 (1998), pp. 207-236. | MR 1619117 | Zbl 0918.35067
,[128] Contributions to the session on Problems in Hysteresis, In: Nonlinear Analysis, Proceedings of the First World Congress of Nonlinear Analysts (ed. ), De Gruyter, Berlin (1996), 797-806. | Zbl 0858.47039
- - - - - ,[129] 1584. Springer, Berlin 1994. | MR 1321829
- - - - ( , ed.), Phase Transitions and Hysteresis, Lecture Notes in Mathematics, vol.[130] Models of Hysteresis, Proceedings of a meeting held in Trento in 1991. Longman, Harlow 1993. | MR 1235109 | Zbl 0785.00016
(ed.),[131]
- - , Géométrie différentielle, éléments finis, modèles d'hystérésis, Eyrolles, Paris1991.[132] Solution périodique de l'équation de la ferrorésonance avec hystérésis, C.R. Acad. Sci. Paris, Serie A, 263 (1966), 497-499. | MR 201106 | Zbl 0152.42103
,[133] Modèle mathématique d'hystérésis et application aux systèmes à un degré de liberté, These, Marseille1969. | Zbl 0237.73020
,[134] Optimal control of ordinary differential equations with nonlinearities of hysteresis type. In: Automation and Remote Control, 52 (1991) and 53 (1992). | MR 1031251 | Zbl 0691.49025
, Optimale Steuerung von gewohnlichen Differentialgleichungen mit Nichtlinearitaten vom Hysteresis-Typ, Habilitations Schrift. Lang, Frankfurt am Main1987. English translation:[135] On a characterization of the Preisach model for hysteresis, Rend. Sem. Mat. Padova, 83 (1990), 153-163. | MR 1066436 | Zbl 0719.47053
,[136] On uniqueness of an initial-problem for ODE with hysteresis, NoDEA, 4 (1997), 391-399. | MR 1458534 | Zbl 0882.34004
- :[137] Une géneralisation vectorielle du modèle de Preisach pour l'hystérésis, C. R. Acad. Sci. Paris, Serie I, 297 (1983), 437-440. | MR 732853 | Zbl 0546.35068
- ,[138] | Zbl 0424.01002
, The evolution of mechanics, Sijthoff and Noordhoff, Alphen aan den Rijn, 1980. Original edition: L'évolution de la méchanique. Joanin, Paris1903.[139] On uniqueness for evolution problems with hysteresis, In: Mathematical Models for Phase Change Problems ( , ed.) (Birkhauser, Basel 1989), 377-388. | MR 1038080 | Zbl 0701.35009
,[140] Identification of hysteresis loops, J. Comp. Phys., 78 (1988), 215-230. | MR 959083 | Zbl 0659.65125
- - ,[141] Some applications of statistical methods to describing deformations of bodies, Izv. Akad. Nauk S.S.S.R., Techn. Ser., 9 (1944), 580-590 (Russian).
,[142] Uber Magnetisierung durch schnellverlaufende Strome und die, Wirkungsweise des Rutherford-Marconischen Magnetdetektors. Ann. Phys., 17 (1905), 861-890.
,[143] Hysterant operator, Soviet Math. Soviet Dokl., 11 (1970), 29-33. | Zbl 0212.58002
- - - , - ,[144] Mathematical models of hysteresis, Phys. Rev. Letters, 56 (1986), 1518-1521.
,[145] Mathematical models of hysteresis, I.E.E.E. Trans. Magn., 22 (1986), 603-608.
,[146] On the description of anisotropic work-hardening, J. Mech. Phys. Solids, 15 (1967), 163-175.
,[147] A model for a body with shape-memory, Arch. Rational Mech. Anal., 70 (1979), 61-77. | MR 535632
,[148] On the size of hysteresis in pseudoelasticity, Continuum Mech. Thermodyn., 1 (1989), 125-142. | MR 1050819
,[149] Theorie des lois d’aimantation de Lord Rayleigh. I. Les déplacements d’une paroi isolée; II. Multiples domaines et champ coercive, Cahiers de Physique, 12 (1942), 1-20; 13 (1943), 18-30.
,[150] Spannungverteilung in plastischen Körpern, In: Proc. 1st Intern. Congr. Appl. Mech. Delft (1924), pp. 43-54.
:[151] Ein Gedankenmodell zur kinetischen Theorie der festen Körper, Z. Angew. Math. Mech., 8 (1928), 85-106. | JFM 54.0847.04
,[152] Über die magnetische Nachwirkung, Z. Physik, 94 (1935), 277-302.
,[153] On the behaviour of iron and steel under the operation of feeble magnetic forces, Phil. Mag., 23 (1887), 225-248. | JFM 19.1131.04
,[154] Numerical approximation of hysteresis problems, I.M.A. J. Numer. Anal., 5 (1985), 447-463. | MR 816068 | Zbl 0608.65082
- ,[155] Numerical approximation of the Preisach model for hysteresis, Math. Model. and Numer. Anal., 23 (1989), 335-356. | MR 1001333 | Zbl 0672.65115
- ,[156] A model for hysteresis of distributed systems, Ann. Mat. Pura Appl., 131 (1982), 203-231. | MR 681564 | Zbl 0494.35052
,[157] On the Preisach model for hysteresis, Nonlinear Analysis, T.M.A., 9 (1984), 977-996. | MR 760191 | Zbl 0563.35007
,[158] Hysteresis and semigroups, In: Models of hysteresis ( , ed.), Longman, Harlow (1993), pp. 192-206. | MR 1235125 | Zbl 0834.35033
,[159] Modified Landau-Lifshitz equation for ferromagnetism, Physica B, 233 (1997), 365-369.
,[160] Etude de l’aimantation initiale en fonction de la température (suite et fin), Arch. Sci. Phys. Nat., (Genève), 42 (1916), 449-470.
- ,[161] | MR 390843 | Zbl 0328.47035
, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden1976.[162] Equations d’Évolution dans un Espace de Banach Quelconque et Applications, Thèse, Orsay 1972.
,[163] On the dynamics of deformable ferromagnets 1. Global weak solutions for soft ferromagnets at rest, Preprint, 1999. | Zbl 1097.74017
- - ,[164] | MR 348562 | Zbl 0252.47055
, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam1973.[165]
, Micromagnetics, Krieger, Huntington1978.[166] | MR 959730 | Zbl 0972.80500
- , Conduction of heat in solids, Clarendon Press and Oxford University Press, New York, 1988.[167] | MR 464857 | Zbl 0298.73001
- , Les Inéquations en Mécanique et en Physique, Dunod, Paris1972.[168] On the theory of dispersion of magnetic permeability in ferromagnetic bodies, Physik. Z. Sowietunion, 8 (1935), 153-169.
- ,[169] | MR 475051 | Zbl 0080.19702
- , Statistical physics, Pergamon Press, Oxford1969.[170] | MR 259693 | Zbl 0189.40603
, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris1969.[171] On Landau-Lifshitz equations in ferromagnetism, Japan J. Appl. Math., 2 (1985), 69-84. | MR 839320 | Zbl 0613.35018
,[172] L’hypothèse du champ moléculaire et la proprièté ferromagnétique, J. Physique, 6 (1907), 661-690.
,