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The Quenching Phenomena for the Cauchy Problem of Semilinear Parabolic Equations

✍ Scribed by Quiyi Dai; Zeng Xianzhong

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
104 KB
Volume
175
Category
Article
ISSN
0022-0396

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The present paper is concerned with the global solvability of the Cauchy problem for the quasilinear parabolic equations with two independent variables: Ε½ . Ε½ . u s a t, x, u, u u q f t, x, u, u . We investigate the case of the arbitrary order < < of growth of the function f t, x, u, p with respect

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It is shown that there exists a critical exponent p \* > 1 for the bipolar blowup in the following sense. If 1 < p ≀ p \* , then there exist arbitrarily small initial data such that the solution exhibits the bipolar blowup, whereas if p > p \* , then the bipolar blowup does not occur for any suffici