Translator Disclaimer
1998 Global existence and nonexistence for a parabolic system with nonlinear boundary conditions
Julio D. Rossi, Noemi Wolanski
Differential Integral Equations 11(1): 179-190 (1998).

Abstract

We find both necessary and sufficient conditions on the nonnegative increasing functions $f$ and $g$ so that positive solutions of $$ \begin{matrix} u_t=\Delta u+h(u,v)\qquad &v_t=\Delta v+r(u,v) \qquad &\text {in }\Omega\times (0,T)\\ \frac{\partial}{\partial\nu} u=f(v) \qquad &\frac{\partial}{\partial\nu} v=g(u)\qquad &\text {on } \partial\Omega\times (0,T) \end{matrix} $$ exist globally in time. We assume throughout that $h$ and $r$ are nonnegative, smooth and $\frac{h(u,v)}u$, $\frac{r(u,v)}v$ are globally bounded.

Citation

Download Citation

Julio D. Rossi. Noemi Wolanski. "Global existence and nonexistence for a parabolic system with nonlinear boundary conditions." Differential Integral Equations 11 (1) 179 - 190, 1998.

Information

Published: 1998
First available in Project Euclid: 1 May 2013

zbMATH: 1004.35012
MathSciNet: MR1608013

Subjects:
Primary: 35K60
Secondary: 35B60

Rights: Copyright © 1998 Khayyam Publishing, Inc.

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.11 • No. 1 • 1998
Back to Top