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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The rate of spatial decay of nonnegative solutions of nonlinear parabolic equations and inequalities


Author: Alan V. Lair
Journal: Proc. Amer. Math. Soc. 112 (1991), 1077-1081
MSC: Primary 35K85; Secondary 35B05, 35K55
MathSciNet review: 1059627
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Abstract: Let $ L$ be a uniformly parabolic linear partial differential operator. We show that nonnegative solutions of the differential inequality $ Lu \leq c(u + \vert\nabla u\vert)$ on $ {{\mathbf{R}}^n} \times (0,T)$ for which $ u(x,T) = {\mathbf{0}}(\exp {\text{(}} - \delta \vert x{\vert^2}))$ must be identically zero if the constant $ \delta $ is sufficiently large. An analogous result is given for nonlinear systems.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1059627-3
PII: S 0002-9939(1991)1059627-3
Article copyright: © Copyright 1991 American Mathematical Society