ASYMPTOTIC BEHAVIOR FOR A NONLOCAL DIFFUSION EQUATION WITH ABSORPTION AND NONINTEGRABLE INITIAL DATA. THE SUPERCRITICAL CASE

In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction —u p , p > 1 and set in ℝ N . We consider a bounded, nonnegative initial datum u₀ that behaves like a negative power at infinity...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2011-04, Vol.139 (4), p.1421-1432
Main Authors: TERRA, JOANA, WOLANSKI, NOEMI
Format: Article
Language:English
Subjects:
Diffusion coefficient
Exact sciences and technology
Fourier transformations
General mathematics
General, history and biography
Heat equation
Infinity
Mathematical analysis
Mathematics
Partial differential equations
Preliminary estimates
Sciences and techniques of general use
Uniqueness
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Summary:In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction —u p , p > 1 and set in ℝ N . We consider a bounded, nonnegative initial datum u₀ that behaves like a negative power at infinity. That is, |x| α u₀(x) → A > 0 as |x| → ∞ with 0 < α ≤ N. We prove that, in the supercritical case p > 1+2/α, the solution behaves asymptotically as that of the heat equation (with diffusivity α related to the nonlocal operator) with the same initial datum.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2010-10612-3