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.
@article{BUMI_2000_8_3B_2_375_0, author = {Th\'eodore K. Boni}, title = {On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {3-A}, year = {2000}, pages = {375-409}, zbl = {0964.35070}, mrnumber = {1769993}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2000_8_3B_2_375_0} }
Boni, Théodore K. On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order. Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000) pp. 375-409. http://gdmltest.u-ga.fr/item/BUMI_2000_8_3B_2_375_0/
[1] Dynamic theory of quasilinear parabolic systems III global existence, Math. Z., 202, 2 (1989), 219-254. | MR 1013086 | Zbl 0702.35125
,[2] 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 1648453 | Zbl 0913.35069
,[3] 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 1320001 | Zbl 0822.35074
,[4] A semilinear parabolic system in a bounded domain, Ann. Mat. pura applicata, (IV), Vol. CLXV (1993), 315-336. | MR 1271424 | Zbl 0806.35088
- ,[5] Critical blow up and global existence for a weakly coupled system of reaction-diffusion equations, Arch. Rational Mech. Anal., 129 (1995), 47-100. | MR 1328471 | Zbl 0822.35068
- ,[6] Global existence and nonexistance for parabolic systems with nonlinear boundary conditions, Math. Ann., 284 (1989), 285-305. | MR 1000112 | Zbl 0652.35065
,[7] Non-existence of global solutions to systems of semi-linear parabolic equations, Jour. of Diff. Equat., 104 (1993), 147-168. | MR 1224124 | Zbl 0816.35060
- ,[8] Limiting behavior of a class of nonlinear reaction diffusion equations, Quaterly of Applied Mathematics, 3, Vol. XL (1982), 293-296. | MR 678200 | Zbl 0506.35059
,[9] 840, Springer (1981). | MR 610244 | Zbl 0456.35001
, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol.[10] 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 470481 | Zbl 0285.35035
and ,[11] | MR 219861 | Zbl 0153.13602
- , Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, NJ (1967).[12] 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 1361728 | Zbl 0851.35064
- ,[13] | MR 172076
, Differential- und integral-ungleichungen, Springer, Berlin (1964).