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Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions

✍ Scribed by C.V. Pao

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
703 KB
Volume
88
Category
Article
ISSN
0377-0427

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✦ Synopsis

This paper is concerned with some dynamical property of a reaction-diffusion equation with nonlocal boundary condition. Under some conditions on the kernel in the boundary condition and suitable conditions on the reaction function, the asymptotic behavior of the time-dependent solution is characterized in relation to a finite or an infinite set of constant steady-state solutions. This characterization is determined solely by the initial function and it leads to the stability and instability of the various steady-state solutions. In the case of finite constant steady-state solutions, the time-dependent solution blows up in finite time when the initial function is greater than the largest constant solution. Also discussed is the decay property of the solution when the kernel function in the boundary condition possesses alternating sign in its domain. (~) 1998 Elsevier Science B.V. All rights reserved.

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