Front propagation for reaction-diffusion equations of bistable type
Barles, G. ; Bronsard, L. ; Souganidis, P. E.
Annales de l'I.H.P. Analyse non linéaire, Tome 9 (1992), p. 479-496 / Harvested from Numdam
Publié le : 1992-01-01
@article{AIHPC_1992__9_5_479_0,
     author = {Barles, Guy and Bronsard, Lia and Souganidis, Panagiotis E.},
     title = {Front propagation for reaction-diffusion equations of bistable type},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {9},
     year = {1992},
     pages = {479-496},
     mrnumber = {1191007},
     zbl = {0794.35076},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1992__9_5_479_0}
}
Barles, G.; Bronsard, L.; Souganidis, P. E. Front propagation for reaction-diffusion equations of bistable type. Annales de l'I.H.P. Analyse non linéaire, Tome 9 (1992) pp. 479-496. http://gdmltest.u-ga.fr/item/AIHPC_1992__9_5_479_0/

[AC] S. Allen and J. Cahn, A Microscopic Theory for Antiphase Boundary Motion and its Application to Antiphase Domain Coarsening, Acta Metall., Vol. 27, 1979, pp. 1084-1095.

[AW] D.G. Aronson and H. Weinberger, Multidimensional Nonlinear Diffusion Arising in Population Genetics, Adv. Math., Vol. 30, 1978, pp. 33-76. | MR 511740 | Zbl 0407.92014

[B] G. Barles, A Remark on a Flame Propagation Model, Rapport I.N.R.I.A., #464, 1985.

[BES] G. Barles, L.C. Evans and P.E. Souganidis, Wavefront Propagation for Reaction-Diffusion Systems of PDE, Duke U. Math. J., Vol. 61, 1990. | MR 1084462 | Zbl 0749.35015

[BP] G. Barles and B. Perthame, Exit Time Problems in Optimal Control and the Vanishing Viscosity Method, S.I.A.M. J. Cont. Opt., Vol. 26, 1988, pp. 113-148. | MR 957658 | Zbl 0674.49027

[BS] G. Barles and P.E. Souganidis, Convergence of Approximation Schemes for Fully Nonlinear Second Order Equations, J. Asympt. Analysis, 1991, pp. 271-283. | MR 1115933 | Zbl 0729.65077

[BSS] G. Barles, M.H. Soner and P.E. Souganidis, in preparation.

[BK1] L. Bronsard and R.V. Kohn, Motion by Mean Curvature as the Singular Limit of Ginzburg-London Dynamics, J. Diff. Eq. (to appear). | Zbl 0735.35072

[BK2] L. Bronsard and R.V. Kohn, On the Slowness of Phase Boundary Motion in One Space Dimension, Comm. Pure Appl. Math. (to appear). | MR 1075075 | Zbl 0761.35044

[Ca] G. Caginalp, A Conserved Phase Field System; Implication for Kinetic Undercooling, Phys. Rev. B.(to appear).

[CaF] G. Caginalp and P. Fife, Dynamics of Layered Interfaces Arising from Phase Boundaries, S.I.A.M. J. Applied Math., Vol. 48, 1988, pp. 506-518. | MR 941098

[Ch] X. Chen, Generation and Propagation of the Interface for Reaction-Diffusion Equations, J. Diff. Eq. (to appear). | MR 1153311 | Zbl 0765.35024

[CP] J. Carr and R. Pego, Patterns in Solutions of ut = ∈2uxx-f(u), Comm. Pure Appl. Math., Vol. 42, 1989, pp. 523-576. | MR 997567 | Zbl 0685.35054

[CrIL] M.G. Crandall, H. Ishii and P.-L. Lions, Uniqueness of Viscosity Solutions Revisited, J. Math. Soc. Japan, Vol. 39, 1987, pp. 581-596. | MR 905626 | Zbl 0644.35016

[CrL] M.G. Crandall and P.-L. Lions, Viscosity Solutions of Hamilton-Jacobi Equations, Trans. A.M.S., Vol. 277, 1983, pp. 1-42. | MR 690039 | Zbl 0599.35024

[DS1] P. Demottoni and M. Schatzman, Geometrical Evolution of Developed Interfaces (preprint). | Zbl 0797.35077 | Zbl 0840.35010

[DS2] P. Demottoni and M. Schatzman, Development of Interfaces in RN (preprint). | Zbl 0725.35009

[EI] L.C. Evans and H. Ishii, A PDE Approach to Some Asymptotic Problems Concerning Random Differential Equations with Small Noise Intensities, Ann. Inst. H. Poincaré, A.N.L., Vol. 2, 1985, pp. 1-20. | Numdam | MR 781589 | Zbl 0601.60076

[ES1] L.C. Evans and P.E. Souganidis, A PDE Approach to Geometric Optics for Certain Reaction-Diffusion Equations, Ind. Un. Math. J., Vol. 38, 1989, pp. 141- 172. | MR 982575 | Zbl 0692.35014

[ES2] L.C. Evans and P.E. Souganidis, A PDE Approach to Certain Large Deviation Problems for Systems of Parabolic Equations, A.N.L., Contributions en l'honneur de J.-J. Moreau, Gauthier-Villars, 1989. | Numdam | MR 1019116 | Zbl 0679.60040

[ESS] L.C. Evans, H.M. Soner and P.E. Souganidis, The Allen-Cahn Equation and Generalized Motion by Mean Curvature (in preparation).

[FH] P.C. Fife and L. Hsiao, The Generation and Propagation of Internal Layers, J. Non-Linear Anal. (to appear). | Zbl 0685.35055

[FH] G. Fusco and J. Hale, Slow Motion Manifold, Dormant Instability and Singular Perturbation, J. Dyn. and Diff. Eqs., Vol. 1, 1989, pp. 75-94. | MR 1010961 | Zbl 0684.34055

[Fi] P. Fife, Dynamics of Internal Layers and Diffusive Interfaces, C.B.M.S.-N.S.F., Regional Conference Series in Applied Math., No. 53, S.I.A.M., Philadelphia. | MR 981594 | Zbl 0684.35001

[F1] W.H. Fleming, Stochastic Control for Small Noise Intensities, S.I.A.M. J. Control., Vol. 9, 1971, pp. 473-517. | MR 304045 | Zbl 0204.47402 | Zbl 0218.93024

[FlS] W.H. Fleming and P.E. Souganidis, PDE-Viscosity Solution Approach to Some Problems of Large Deviations, An. Scuola Norm. Sup., Vol. 13, 1986, pp. 171-192. | Numdam | MR 876121 | Zbl 0622.60032

[Fr1] M.I. Freidlin, Limit Theorems for Large Deviations and Reaction-Diffusion Equations, Annals of Prob., Vol. 13, 1985, pp. 639-675. | MR 799415 | Zbl 0576.60070

[Fr2] M.I. Freidlin, Functional Integration and Partial Differential Equations, Annals of Math. Studies 109, Princeton University Press, Princeton, 1985. | MR 833742 | Zbl 0568.60057

[G] J. Gärtner, Bistable Reaction-Diffusion Equations and Excitable Media, Math. Nachr., Vol. 112, 1983, pp. 125-152. | MR 726855 | Zbl 0548.35069

[GSS] J. Gunton, M. San Miguel and P. Sahni, The Dynamics of First-Order Phase Transitions, in Phase Transitions and Critical Phenomena, C. DOMB and J. LIEBOWITZ Eds., Vol. 8, 1983, pp. 267-466. | MR 794319

[I] H. Ishii, Hamilton-Jacobi Equations with Discontinuous Hamiltonians on Arbitrary Open Sets, Bull. Fac. Sci. Eng. Chuo Univ., Vol. 28, 1985, pp. 33-77. | MR 845397 | Zbl 0937.35505

[L] P.-L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, Boston, 1982. | MR 667669 | Zbl 0497.35001

[LSV] P.-L. Lions, P.E. Souganidis and J.L. Vazquez, The Relation Between the Porous-Medium and Eikonal Equations in Several Space Dimensions, Rev. Mat. Iberoamericana, Vol. 3, 1987, pp.275-310. | MR 996819 | Zbl 0697.35012

[P] R. Rpego,Front Migration in the Nonlinear Cahn-Hilliard Equation, Proc. R. Soc. Lond., Vol. A 422, 1989, pp. 261-278. | MR 997638 | Zbl 0701.35159

[RSK] J. Rubinstein, P. Sternberg and J.B. Keller, Fast Reaction, Slow Diffusion, and Curve Shortening, S.I.A.M. Appl. Math., Vol. 49, 1989, pp. 116-133. | MR 978829 | Zbl 0701.35012