Volume 36, Issue 1
Equivalence Relation Between Initial Values and Solutions for Evolution $p$-Laplacian Equation in Unbounded Space

Commun. Math. Res., 36 (2020), pp. 51-67.

Published online: 2020-03

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• 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.

• Keywords

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

35K55, 35B40

wanglw08@163.com (Liangwei Wang)

yjx@scnu.edu.cn (Jingxue Yin)

zhoulanghao8@163.com (Langhao Zhou)

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@Article{CMR-36-51, author = {Wang , Liangwei and Yin , Jingxue and Zhou , Langhao}, title = {Equivalence Relation Between Initial Values and Solutions for Evolution $p$-Laplacian Equation in Unbounded Space }, journal = {Communications in Mathematical Research }, year = {2020}, volume = {36}, number = {1}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0003}, url = {http://global-sci.org/intro/article_detail/cmr/15789.html} }
TY - JOUR T1 - Equivalence Relation Between Initial Values and Solutions for Evolution $p$-Laplacian Equation in Unbounded Space AU - Wang , Liangwei AU - Yin , Jingxue AU - Zhou , Langhao JO - Communications in Mathematical Research VL - 1 SP - 51 EP - 67 PY - 2020 DA - 2020/03 SN - 36 DO - http://doi.org/10.4208/cmr.2020-0003 UR - https://global-sci.org/intro/article_detail/cmr/15789.html KW - Asymptotic behavior, evolution $p$-Laplacian equation, unbounded function, propagation estimate, growth estimate. AB -

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.

Liangwei Wang, Jingxue Yin & Langhao Zhou. (2020). Equivalence Relation Between Initial Values and Solutions for Evolution $p$-Laplacian Equation in Unbounded Space . Communications in Mathematical Research . 36 (1). 51-67. doi:10.4208/cmr.2020-0003
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