Equivalence Relation Between Initial Values and Solutions for Evolution $p$-Laplacian Equation in Unbounded Space

Authors

  • Liangwei Wang College of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404000, China.
  • Jingxue Yin School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong, 510631, P. R. China
  • Langhao Zhou College of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404000, China.

DOI:

https://doi.org/10.4208/cmr.2020-0003

Keywords:

Asymptotic behavior, evolution $p$-Laplacian equation, unbounded function, propagation estimate, growth estimate.

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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Published

2020-03-17

Issue

Vol. 36 No. 1 (2020)

Section

Articles