Blow-up of sign-changing solutions to quasilinear parabolic equations

被引：0
|
作者：
S. I. Pohozaev
机构：
[1] Russian Academy of Sciences,Steklov Mathematical Institute
来源：
Proceedings of the Steklov Institute of Mathematics | 2010年 / 269卷
关键词：
Cauchy Problem; Parabolic Equation; STEKLOV Institute; Nonlinear Wave Equation; QUASILINEAR Equation;
D O I：
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中图分类号：
学科分类号：
摘要：
We study the blow-up of sign-changing solutions to the Cauchy problem for quasilinear parabolic equations of arbitrary order. Our approach is based on H. Levine’s remarkable idea of constructing a concavity inequality for a negative power of a standard positive definite functional. Combining this with the nonlinear capacity method, which is based on the choice of optimal test functions, we find conditions for the blow-up of solutions to the problems under consideration.
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页码：208 / 217
页数：9
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