Differential and Integral Equations

On the qualitative behaviour of some semilinear parabolic problems

Joachim Escher

Full-text: Open access


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

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

First available in Project Euclid: 20 May 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation