Differential and Integral Equations

Stability of stationary solutions of nonlocal reaction-diffusion equations in $m$-dimensional space

Abstract

We consider nonlocal reaction--diffusion equations in $m$--dimensional space. An existence theory is established using standard techniques. It is shown that when local monotonicity conditions are imposed, the stationary solutions that can be stable are those that are stable for an auxiliary local problem. This contrasts with what happens in the general case, where more complex solutions may be stable. An example of such a case is given. These results are obtained using comparison techniques and a generalization of previous results to the $m$--dimensional case.

Article information

Source
Differential Integral Equations Volume 13, Number 1-3 (2000), 265-288.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356124300

Mathematical Reviews number (MathSciNet)
MR1811959

Zentralblatt MATH identifier
1038.35030

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35A07 35B35: Stability 35B40: Asymptotic behavior of solutions

Citation

Freitas, Pedro; Vishnevskii, Mikhail P. Stability of stationary solutions of nonlocal reaction-diffusion equations in $m$-dimensional space. Differential Integral Equations 13 (2000), no. 1-3, 265--288. https://projecteuclid.org/euclid.die/1356124300.