MISC

2009年1月

Solutions with moving singularities for a semilinear parabolic equation

JOURNAL OF DIFFERENTIAL EQUATIONS
  • Shota Sato
  • ,
  • Eiji Yanagida

246
2
開始ページ
724
終了ページ
748
記述言語
英語
掲載種別
DOI
10.1016/j.jde.2008.09.004
出版者・発行元
ACADEMIC PRESS INC ELSEVIER SCIENCE

We consider the Cauchy problem for a semilinear heat equation with power nonlinearity. It is known that the equation has a singular steady state in some parameter range. Our concern is a solution with a moving singularity that is obtained by perturbing the singular steady state. By formal expansion, it turns Out that the remainder term must satisfy a certain parabolic equation with inverse-square potential. From the well-posedness of this equation, we see that there appears a critical exponent. Paying attention to this exponent, for a prescribed motion of the singular point and suitable initial data, we establish the time-local existence, uniqueness and comparison principle for such singular solutions. We also consider solutions with multiple singularities. (C) 2008 Elsevier Inc. All rights reserved.

リンク情報
DOI
https://doi.org/10.1016/j.jde.2008.09.004
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000261714900012&DestApp=WOS_CPL
ID情報
  • DOI : 10.1016/j.jde.2008.09.004
  • ISSN : 0022-0396
  • Web of Science ID : WOS:000261714900012

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