Global attractor for reaction-diffusion equations with supercritical nonlinearity in unbounded domains

Date

2016-03-04

Authors

Zhang, Jin
Zhang, Chang
Zhong, Chengkui

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Publisher

Texas State University, Department of Mathematics

Abstract

We consider the existence of global attractor for the inhomogeneous reaction-diffusion equation ut - ∆u - V(x)u + |u|p-2 u = g, in ℝn x ℝ+, u(0) = u0 ∈ L2(ℝn) ∩ Lp(ℝn), where p > 2n/n-2 is supercritical and V(x) satisfies suitable assumptions. Since -∆ is not positive definite in H1(ℝn), the Gronwall inequality can not be derived and the corresponding semigroup does not possess bounded absorbing sets in L2(ℝn). Thus, by a special method, we prove that the equation has a global attractor in Lp(ℝn), which attracts any bounded subset in L2(ℝn) ∩ Lp(ℝn).

Description

Keywords

Global attractor, Inhomogeneous reaction-diffusion equation, Unbounded domain, Supercritical nonlinearity

Citation

Zhang, J., Zhang, C., & Zhong, C. (2016). Global attractor for reaction-diffusion equations with supercritical nonlinearity in unbounded domains. <i>Electronic Journal of Differential Equations, 2016</i>(63), pp. 1-9.

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Attribution 4.0 International

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