Self-similar solutions for a quenching problem with spatially dependent nonlinearity

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Journal Article > Item 987654321/108413

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Title:	Self-similar solutions for a quenching problem with spatially dependent nonlinearity
Authors:	Jong-Shenq Guo;Yoshihisa Morita;Shoji Yotsutani
Keywords:	Self-similar solution;Slow orbit;Pohozaev's type identity;Backward solution
Date:	2016-12-01
Issue Date:	2016-11-25 02:10:39 (UTC+8)
Publisher:	Pergamon Press
Abstract:	This paper is devoted to the study of the self-similar solutions for a semilinear parabolic equation with spatially dependent nonlinearity which arises in the model of micro-electro mechanical system. We first provide a result on the non-existence of slow orbit for a certain range of parameters. Next, we prove the existence of backward solutions with the desired polynomial growth condition at infinity to the associated equation by a fixed point argument. Then we give a detailed analysis of the behavior of global solutions at the origin. Finally, as an application of the above results, we prove a uniqueness theorem.
Relation:	Nonlinear Analysis: Theory, Methods & Applications 147, p.45-62
DOI:	10.1016/j.na.2016.08.026
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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