Differential and Integral Equations

Global existence and nonexistence for a parabolic system with nonlinear boundary conditions

Julio D. Rossi and Noemi Wolanski

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Differential Integral Equations, Volume 11, Number 1 (1998), 179-190.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367414142

Mathematical Reviews number (MathSciNet)
MR1608013

Zentralblatt MATH identifier
1004.35012

Subjects
Primary: 35K60: Nonlinear initial value problems for linear parabolic equations
Secondary: 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx]

Citation

Rossi, Julio D.; Wolanski, Noemi. Global existence and nonexistence for a parabolic system with nonlinear boundary conditions. Differential Integral Equations 11 (1998), no. 1, 179--190. https://projecteuclid.org/euclid.die/1367414142


Export citation