Differential and Integral Equations

On the qualitative behaviour of some semilinear parabolic problems

Joachim Escher

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Abstract

This paper is concerned with semilinear reaction-diffusion systems under nonlinear dynamical boundary conditions. We will prove that such problems are well-posed on some Bessel potential spaces and that the corresponding solution defines a local semiflow on these spaces. This result will enable us to investigate the dynamical properties of the solutions under discussion. In particular, we will prove some conclusions concerning global existence and blow up phenomena as well as singular perturbation results.

Article information

Source
Differential Integral Equations, Volume 8, Number 2 (1995), 247-267.

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369083468

Mathematical Reviews number (MathSciNet)
MR1296123

Zentralblatt MATH identifier
0814.35053

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35Bxx: Qualitative properties of solutions 35D05

Citation

Escher, Joachim. On the qualitative behaviour of some semilinear parabolic problems. Differential Integral Equations 8 (1995), no. 2, 247--267. https://projecteuclid.org/euclid.die/1369083468


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