2009年1月
Solutions with moving singularities for a semilinear parabolic equation
JOURNAL OF DIFFERENTIAL EQUATIONS
- ,
- 巻
- 246
- 号
- 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
- ID情報
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- DOI : 10.1016/j.jde.2008.09.004
- ISSN : 0022-0396
- Web of Science ID : WOS:000261714900012