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Self-Similar Subsolutions and Blowup for Nonlinear Parabolic Equations

✍ Scribed by Philippe Souplet; Fred B Weissler

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
229 KB
Volume
212
Category
Article
ISSN
0022-247X

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✦ Synopsis

For a wide class of nonlinear parabolic equations of the form u y ⌬ u s t Ž . F u, ٌu , we prove the nonexistence of global solutions for large initial data. We also estimate the maximal existence time. To do so we use a method of comparison with suitable blowing up self-similar subsolutions. As a consequence, we improve several known results on u y ⌬ u s u p , on generalized Burgers' equations, and on t other semilinear equations. This method can also apply to degenerate equations of porous medium type and provides a unified treatment for a large class of problems, both semilinear and quasilinear.

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