Extinction and decay estimates for viscous Hamilton-Jacobi equations in ℝ^{ℕ}

Benachour, Said; Laurençot, Philippe; Schmitt, Didier

doi:10.1090/S0002-9939-01-06140-8

Extinction and decay estimates for viscous Hamilton-Jacobi equations in ${\mathbb {R}}^N$
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by Said Benachour, Philippe Laurençot and Didier Schmitt PDF

Proc. Amer. Math. Soc. 130 (2002), 1103-1111 Request permission

Abstract:

We consider non-negative and integrable classical solutions to the Cauchy problem $u_t-\Delta u+\vert \nabla u\vert ^p=0$ when $p\in (0,+\infty )$. For $p\in (0,N/(N+1))$ we prove that any such solution vanishes identically after a finite time. For higher values of $p$ temporal decay estimates are obtained.

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