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Lp-type pullback attractors for a semilinear heat equation on time-varying domains

Part of: Hyperbolic equations and systems Parabolic equations and systems Partial differential equations

Published online by Cambridge University Press:  02 September 2015

Chunyou Sun  and
Yanbo Yuan
Chunyou Sun
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China (sunchy@lzu.edu.cn; yuanyb11@lzu.edu.cn)
Yanbo Yuan
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China (sunchy@lzu.edu.cn; yuanyb11@lzu.edu.cn)
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Abstract

We present a new method for investigating the Lp-type pullback attractors (2 ≤ p < ∞) of a semilinear heat equation on a time-varying domain under quite general assumptions on the nonlinear and forcing terms. The existing approach does not appear applicable here as it is impossible to show the existence of a pullback absorbing set in Lp space when p is large. A new asymptotic decomposition scheme for a non-autonomous pullback attractor has been introduced. The abstract results and preliminary lemmas are also of independent interest and applicable to other systems.

Keywords

non-autonomous dynamical systemsasymptotic decompositionpullback attractorssemilinear heat equationtime-varying domain

MSC classification

Primary: 35K57: Reaction-diffusion equations
Secondary: 35L05: Wave equation 35B40: Asymptotic behavior of solutions 35B41: Attractors
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 5 , October 2015 , pp. 1029 - 1052
Copyright
Copyright © Royal Society of Edinburgh 2015 

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