Hokkaido Mathematical Journal

SNOUSSI Seifeddine, TAYACHI Slim,

Large time behavior of solutions for parabolic equations with nonlinear gradient terms.

Hokkaido Mathematical Journal, 36 (2007) pp.311-344

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Abstract

In this paper we prove the global existence of mild solutions for the semilinear parabolic equation $u_t=\Delta u+a|\nabla u|^q+b|u|^{p-1}u, t>0, x \in \mathbb R^n, n \geq 1,$ $a \in \mathbb R, b \in \mathbb R, p>1+(2/n),$ $(n+2)/(n+1)

MSC(Primary)35K55
MSC(Secondary)35K65, 35K15, 35B40
Uncontrolled KeywordsSemilinear parabolic equations, Global solutions, Large time behavior, Self-similar solutions, Nonlinear gradient term, Viscous Hamilton–Jacobi equation