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

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dc.contributor.authorZhang, Jin
dc.contributor.authorZhang, Chang
dc.contributor.authorZhong, Chengkui
dc.date.accessioned2023-06-15T17:40:38Z
dc.date.available2023-06-15T17:40:38Z
dc.date.issued2016-03-04
dc.description.abstractWe 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).
dc.description.departmentMathematics
dc.formatText
dc.format.extent9 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationZhang, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16936
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2016, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectGlobal attractor
dc.subjectInhomogeneous reaction-diffusion equation
dc.subjectUnbounded domain
dc.subjectSupercritical nonlinearity
dc.titleGlobal attractor for reaction-diffusion equations with supercritical nonlinearity in unbounded domainsen_US
dc.typeArticle

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