Extinction and Decay Estimates for Viscous Hamilton-Jacobi Equations in RN

We consider non-negative and integrable classical solutions to the Cauchy problem$u_t -\Delta u +| \nabla u|^p = 0$when p ∈ (0, +∞). For p ∈ (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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Veröffentlicht in:	Proceedings of the American Mathematical Society 2002-04, Vol.130 (4), p.1103-1111
Hauptverfasser:	Benachour, Said, Laurencot, Philippe, Schmitt, Didier
Format:	Artikel
Sprache:	eng
Schlagworte:	Cauchy problem Decreasing functions Differential variability inequalities Exact sciences and technology Heat equation Mathematical analysis Mathematical theorems Mathematics Partial differential equations Polynomials Sciences and techniques of general use
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Zusammenfassung:	We consider non-negative and integrable classical solutions to the Cauchy problem$u_t -\Delta u +\| \nabla u\|^p = 0$when p ∈ (0, +∞). For p ∈ (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.
ISSN:	0002-9939 1088-6826