Equivalence Relation Between Initial Values and Solutions for Evolution $p$-Laplacian Equation in Unbounded Space
Year: 2020
Author: Liangwei Wang, Jingxue Yin, Langhao Zhou
Communications in Mathematical Research , Vol. 36 (2020), Iss. 1 : pp. 51–67
Abstract
In this paper, an equivalence relation between the $ω$-limit set of initial values and the $ω$-limit set of solutions is established for the Cauchy problem of evolution $p$-Laplacian equation in the unbounded space $\mathcal{Y}$$σ$($ℝ$$N$). To overcome the difficulties caused by the nonlinearity of the equation and the unbounded solutions, we establish the propagation estimate and the growth estimate for the solutions. It will be demonstrated that the equivalence relation can be used to study the asymptotic behavior of solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2020-0003
Communications in Mathematical Research , Vol. 36 (2020), Iss. 1 : pp. 51–67
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Asymptotic behavior evolution $p$-Laplacian equation unbounded function propagation estimate growth estimate.