Singular behavior in nonlinear parabolic equations

Wei Ming Ni, Paul Sacks

Research output: Contribution to journalArticlepeer-review

81 Scopus citations

Abstract

In this paper, we study the well-posedness of the initial-boundary value problems of some quasilinear parabolic equations, namely, nonlinear heat equations and the porous medium equation in the fast-diffusion case. We establish nonuniqueness (local in time) and/or nonregularizing effect of these equations in some critical cases. The key which leads to the resolution of these problems is to study some singular solutions of the elliptic counterparts of these parabolic problems (the so-called Absolutions of the Lane-Emden equations in astrophysics).

Original languageEnglish (US)
Pages (from-to)657-671
Number of pages15
JournalTransactions of the American Mathematical Society
Volume287
Issue number2
DOIs
StatePublished - Feb 1985

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