Boni, Théodore K.:
On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order
Bollettino dell'Unione Matematica Italiana Serie 8 3-B (2000), fasc. n.2, p. 375-409, Unione Matematica Italiana (English)
pdf (368 Kb), djvu (364 Kb). | MR1769993 | Zbl 0964.35070
Sunto
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.
Referenze Bibliografiche
[1]
H. AMANN,
Dynamic theory of quasilinear parabolic systems III global existence,
Math. Z.,
202, 2 (
1989), 219-254. |
MR 1013086 |
Zbl 0702.35125[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 1648453 |
Zbl 0913.35069[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 1320001 |
Zbl 0822.35074[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 1271424 |
Zbl 0806.35088[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 1328471 |
Zbl 0822.35068[6]
J. ESCHER,
Global existence and nonexistance for parabolic systems with nonlinear boundary conditions,
Math. Ann.,
284 (
1989), 285-305. |
MR 1000112 |
Zbl 0652.35065[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 1224124 |
Zbl 0816.35060[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 678200 |
Zbl 0506.35059[9]
D. HENRY,
Geometric theory of semilinear parabolic equations,
Lecture Notes in Mathematics, vol.
840,
Springer (
1981). |
MR 610244 |
Zbl 0456.35001[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 470481 |
Zbl 0285.35035[11]
M. H. PROTTER-
H. F. WEINBERGER,
Maximum principles in differential equations,
Prentice Hall, Englewood Cliffs, NJ (
1967). |
MR 219861 |
Zbl 0153.13602[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 1361728 |
Zbl 0851.35064[13]
W. WALTER,
Differential- und integral-ungleichungen,
Springer, Berlin (
1964). |
MR 172076