# Hokkaido Mathematical Journal

## 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 35K65, 35K15, 35B40 Semilinear parabolic equations, Global solutions, Large time behavior, Self-similar solutions, Nonlinear gradient term, Viscous Hamilton–Jacobi equation