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Transactions of the American Mathematical Society

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

 
 

 

Harnack estimates and extinction profile for weak solutions of certain singular parabolic equations


Authors: E. DiBenedetto and Y. C. Kwong
Journal: Trans. Amer. Math. Soc. 330 (1992), 783-811
MSC: Primary 35B45; Secondary 35B05, 35K55, 35K65
DOI: https://doi.org/10.1090/S0002-9947-1992-1076615-7
MathSciNet review: 1076615
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Abstract: We establish an intrinsic Harnack estimate for nonnegative weak solutions of the singular equation $ (1.1)$ below, for $ m$ in the optimal range $ ((N - 2)_+/N,1)$. Intrinsic means that, due to the singularity, the space-time dimensions in the parabolic geometry must be rescaled by a factor determined by the solution itself. Consequences are, sharp supestimates on the solutions and decay rates as $ t$ approaches the extinction time. Analogous results are shown for $ p$-laplacian type equations.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1076615-7
Article copyright: © Copyright 1992 American Mathematical Society

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