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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A very singular solution of a quasilinear degenerate diffusion equation with absorption


Authors: L. A. Peletier and Jun Yu Wang
Journal: Trans. Amer. Math. Soc. 307 (1988), 813-826
MSC: Primary 35K65; Secondary 35K55
MathSciNet review: 940229
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Abstract | References | Similar Articles | Additional Information

Abstract: The object of this paper is to study the existence of a nonnegative solution of the Cauchy problem

$\displaystyle {u_t} = \operatorname{div} (\vert\nabla u{\vert^{p - 2}}\nabla u) - {u^q},\qquad u(x,\,0) = 0\quad {\text{if}}\;x \ne 0,$

which is more singular at $ (0,\,0)$ than the fundamental solution of the corresponding equation without the absorption term.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0940229-6
PII: S 0002-9947(1988)0940229-6
Article copyright: © Copyright 1988 American Mathematical Society