@article{RSMUP_1992__87__209_0, author = {Vespri, Vincenzo}, title = {Local existence, uniqueness and regularity for a class of degenerate parabolic systems arising in biological models}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, volume = {88}, year = {1992}, pages = {209-244}, mrnumber = {1183909}, zbl = {0755.35059}, language = {en}, url = {http://dml.mathdoc.fr/item/RSMUP_1992__87__209_0} }
Vespri, Vincenzo. Local existence, uniqueness and regularity for a class of degenerate parabolic systems arising in biological models. Rendiconti del Seminario Matematico della Università di Padova, Tome 88 (1992) pp. 209-244. http://gdmltest.u-ga.fr/item/RSMUP_1992__87__209_0/
[1] On the eigenfunctions and the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math., 15 (1962), pp. 119-147. | MR 147774 | Zbl 0109.32701
,[2] Models for mutual attractions and aggregations of motile individuals, L.N.B. 57, Proceedings of Mathematics in Biology and Medicine, Capasso-Grosso-Papaveri Fontana editors, Bari (1983). | Zbl 0591.92025
,[3] A density dependent diffusion system with stable discontinuous stationary solutions, Ann. Mat. Pura Appl., to appear. | Zbl 0673.35054
- - ,[4] On interacting populations that disperse to avoid crowding: the effect of a sedentary colony, J. Math. Biology, 19 (1984), pp. 1-12. | MR 737167 | Zbl 0538.92020
- - - ,[5] On interacting populations that disperse to avoid crowding: preservation of segregation, J. Math. Biology, 23 (1985), pp. 1-13. | MR 821681 | Zbl 0596.35074
- - - ,[6] A density dependent diffusion problem in population dynamics, SIAM J. Math. Anal., 17 (1986), pp. 863-883. | MR 846394 | Zbl 0607.35052
- ,[7] On a degenerate diffusion equation of the form c(z)t = Φ(zx)x with applications to population dynamics, J. Diff. Eqs., 67 (1987), pp. 56-89. | Zbl 0624.35049
- - ,[8] Sulle maggiorazioni in Lp nella teoria delle equazioni ellittiche, Boll. Un. Mat. Ital., 20 (1965), pp. 393-399. | MR 192169 | Zbl 0142.37604
- ,[9] B. TERRENI - V. VESPRI, Analytic semigroups generated by nonvariational elliptic systems of second order under Dirichlet boundary conditions, J. Math. Anal. Appl., 112 (1985), pp. 56-103. | MR 812793 | Zbl 0593.47048
-[10] Generation of analytic semigroups in the LP topology by elliptic operators in Rn, Israel J. Math., 61 (1988), pp. 235-255. | MR 941240 | Zbl 0669.35026
- ,[11] A mathematical model for the 1973 cholera epidemic in the european mediterranean region, Rev. Epidém. Santé Publ., 27 (1979), pp. 121-132.
,[12] Proceedings of mathematics in Biology and Medicine, L.N.S. 57, Bari (1983). | Zbl 0559.00025
- - ,[13] On existence, uniqueness and attractivity of stationary solutions to some quasilinear parabolic systems, L.B.N. 57, Proceedings of Mathematics in Biology and Medicine, Capasso- Grosso-Paveri Fontana editors, Bari (1983). | Zbl 0572.35035
- ,[14] Nonlinear diffusion problems, L.N.S. 1224, Corso CIME, Montecatini Terme (1985). | Zbl 0595.00014
- ,[15] L. A. SEGEL, Model of chemotaxis, J. Theor. Biol., 30 (1971), pp. 225-234.
-[16] Théoremes de trace et d'interpolation - I, Ann. Scuola Norm. Sup. Pisa, 13 (1959), pp. 389-403. | Numdam | MR 119092 | Zbl 0097.09502
,[17] J. PEETRE, Sur une class d'espaces d'interpolation, Publ. I.H.E.S., Paris (1964), pp. 5-68. | Numdam | MR 165343 | Zbl 0148.11403
-[18] On the local dynamical system associated to a fully nonlinear abstract parabolic equation, in Nonlinear Analysis and Applications, V. Laksmikantham editor (1987), pp. 319-326. | MR 912310 | Zbl 0646.47045
,[19] Pattern formation in competition diffusion systems in nonconvex domains, Publ. Res. Inst. Math. Sci. Kyoto Univ., 19 (1983), pp. 1049-1079. | MR 723460 | Zbl 0548.35063
- ,[20] Stationary pattern of some density dependent diffusion systems with competitive dynamics, Hiroshima Math. J., 11 (1981), pp. 621-635. | MR 635042 | Zbl 0483.35045
,[21] A. TESEI, Degenerate parabolic problems in populaction dynamics, Japan J. Appl. Math., 2 (1985), pp. 351-380. | MR 839335
-[22] A. TESEI, Global existence of solutions for a strongly coupled quasilinear parabolic system, Nonlinear Analysis, 14 (1990), pp. 657-690. | MR 1049787 | Zbl 0716.35034
-[23] Spatial segregation of interacting species, J. Theor. Biology, 79 (1979), pp. 83-99. | MR 540951
- - ,[24] On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl., 107 (1985), pp. 16-66. | MR 786012 | Zbl 0589.47042
,[25] Analytic semigroups, degenerate elliptic operators and applications to nonlinear Cauchy problems, Ann. Mat. Pura Appl., 155 (1989), pp. 353-388. | MR 1042844 | Zbl 0709.35065
,[26] Gebrochene potenzen eines elliptischen operator und parabolische differentialgleichungen in raumen Hölderstetiger funktionen, Nachr. Akad. Wiss. Gottingen Math. Phis. Kl., 11 (1972), pp. 231-258. | MR 313636 | Zbl 0251.35052
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