Geodesic
On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order
Bollettino della Unione matematica italiana, Série 8, 3B (2000) no. 2, pp. 375-409.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In questo lavoro sotto queste ipotesi si ottengono alcune condizioni di non esistenza e di esistenza delle soluzioni per alcuni sistemi parabolici semilineari del secondo ordine. Inoltre si studia il comportamento asintotico di alcune soluzioni. 
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Boni, Théodore K. On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order. Bollettino della Unione matematica italiana, Série 8, 3B (2000) no. 2, pp. 375-409. http://geodesic.mathdoc.fr/item/BUMI_2000_8_3B_2_a8/

[1] H. Amann, Dynamic theory of quasilinear parabolic systems III global existence, Math. Z., 202, 2 (1989), 219-254. | MR | Zbl

[2] T. K. Boni, Sur l'explosion et le comportement asymptotique de la solution d'une équation parabolique semi-linéaire du second ordre, C. R. Acad. Paris, t. 326, Série I (1998), 317-322. | MR | Zbl

[3] K. Deng, Global existence and blow up for a system of heat equations with a nonlinear boundary conditions, Math. Meth. in the Appl. Sci., 18 (1995), 307-315. | MR | Zbl

[4] M. Escobedo-M. A. Herrero, A semilinear parabolic system in a bounded domain, Ann. Mat. pura applicata, (IV), Vol. CLXV (1993), 315-336. | MR | Zbl

[5] M. Escobedo-H. A. Levine, Critical blow up and global existence for a weakly coupled system of reaction-diffusion equations, Arch. Rational Mech. Anal., 129 (1995), 47-100. | MR | Zbl

[6] J. Escher, Global existence and nonexistance for parabolic systems with nonlinear boundary conditions, Math. Ann., 284 (1989), 285-305. | MR | Zbl

[7] L. Gang-B. D. Sleeman, Non-existence of global solutions to systems of semi-linear parabolic equations, Jour. of Diff. Equat., 104 (1993), 147-168. | MR | Zbl

[8] C. J. Holland, Limiting behavior of a class of nonlinear reaction diffusion equations, Quaterly of Applied Mathematics, 3, Vol. XL (1982), 293-296. | MR | Zbl

[9] D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer (1981). | MR | Zbl

[10] H. A. Levine and L. E. Payne, Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time, Jour. of Diff. Equat., 16 (1974), 319-334. | MR | Zbl

[11] M. H. Protter-H. F. Weinberger, Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, NJ (1967). | MR | Zbl

[12] J. Rossi-N. Wolanski, Blow-up vs. global existence for a semilinear reactiondiffusion system in a bounded domain, Commun. in PDE., 20 (11 and 12), (1995), 1991-2004. | MR | Zbl

[13] W. Walter, Differential- und integral-ungleichungen, Springer, Berlin (1964). | MR