Global existence and decay for a nonlinear parabolic equation. (English) Zbl 0782.35009

The author studies the global existence and decay of solutions of the semilinear parabolic problem \[ u_ t=\Delta u+\eta|\nabla u|, \quad \eta\neq 0, \qquad u(x,0)=u_ 0(x), \quad x\in\mathbb{R}^ n. \]


35B40 Asymptotic behavior of solutions to PDEs
35K15 Initial value problems for second-order parabolic equations
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