Global attractor for reaction-diffusion equations with supercritical nonlinearity in unbounded domains
Date
2016-03-04
Authors
Zhang, Jin
Zhang, Chang
Zhong, Chengkui
Journal Title
Journal ISSN
Volume Title
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. Electronic Journal of Differential Equations, 2016(63), pp. 1-9.
Rights
Attribution 4.0 International