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A Liouville theorem for vector valued semilinear heat equations with no gradient structure and applications to blow-up

Zaag, Hatem; Nouaili, Nejla (2010), A Liouville theorem for vector valued semilinear heat equations with no gradient structure and applications to blow-up, Transactions of the American Mathematical Society, 362, 7, p. 3391-3434

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00531306/fr/
Date
2010
Journal name
Transactions of the American Mathematical Society
Volume
362
Number
7
Publisher
American Mathematical Society
Pages
3391-3434
Metadata
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Author(s)
Zaag, Hatem cc
Nouaili, Nejla
Abstract (EN)
We prove a Liouville Theorem for a vector valued semilinear heat equation with no gradient structure. Classical tools such as the maximum principle or energy techniques break down and have to be replaced by a new approach. We then derive from this theorem uniform estimates for blow-up solutions of that equation.
Subjects / Keywords
Vector-valued; Heat equation; Uniform estimates; Liouville theorem; Blow-up