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2008 Asymptotic behavior of strong solutions for nonlinear parabolic equations with critical Sobolev exponent
Michinori Ishiwata
Adv. Differential Equations 13(3-4): 349-366 (2008).

Abstract

In this paper, we discuss the asymptotic behavior of solutions of nonlinear parabolic equations in ${\mathbf{R}}^N$ involving critical Sobolev exponent. For the semilinear and subcritical problem, it is well-known that the solution which intersects with the ``stable set'' must be a global one and the solution which enters the "unstable set"feodory should blow up in finite time. But in the critical case, it is not clear that the same result holds or not. In this paper, we show that the same result holds also in the critical case. The proof of our main result requires the method different from that for the subcritical problem and is based on the direct analysis of $L^\infty$-norm of solutions with the aid of the blow up argument and the concentration compactness type argument.

Citation

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Michinori Ishiwata. "Asymptotic behavior of strong solutions for nonlinear parabolic equations with critical Sobolev exponent." Adv. Differential Equations 13 (3-4) 349 - 366, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1171.35331
MathSciNet: MR2482421

Subjects:
Primary: 35K92
Secondary: 35B33, 35B40, 35K20, 35K55

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.13 • No. 3-4 • 2008
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