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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Singular behavior in nonlinear parabolic equations


Authors: Wei-Ming Ni and Paul Sacks
Journal: Trans. Amer. Math. Soc. 287 (1985), 657-671
MSC: Primary 35K60; Secondary 35J65
MathSciNet review: 768731
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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 $ M$-solutions of the Lane-Emden equations in astrophysics).


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DOI: https://doi.org/10.1090/S0002-9947-1985-0768731-8
Article copyright: © Copyright 1985 American Mathematical Society