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Global existence for a vector-valued nonlinear heat equation

โœ Scribed by Mohammed Aassila

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
158 KB
Volume
53
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

In this paper, we are concerned with the global existence, the uniqueness, the nonnegativity of classical solutions of a semilinear parabolic coupled system.

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A Liouville theorem and blowup behavior
A Liouville theorem and blowup behavior for a vector-valued nonlinear heat equation with no gradient structure
โœ Hatem Zaag ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 178 KB ๐Ÿ‘ 1 views

We prove a Liouville theorem for the following heat system whose nonlinearity has no gradient structure: where pq > 1, p โ‰ฅ 1, q โ‰ฅ 1, and | p -q| small. We then deduce a localization property and uniform L โˆž estimates of blowup solutions of this system.