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

Nouaili, Nejla; Zaag, Hatem

doi:10.1090/S0002-9947-10-04902-0

A Liouville theorem for vector valued semilinear heat equations with no gradient structure and applications to blow-up
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by Nejla Nouaili and Hatem Zaag

Trans. Amer. Math. Soc. 362 (2010), 3391-3434

DOI: https://doi.org/10.1090/S0002-9947-10-04902-0

Published electronically: February 17, 2010

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Abstract:

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.

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