Harnack estimates and extinction profile for weak solutions of certain singular parabolic equations
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- by E. DiBenedetto and Y. C. Kwong PDF
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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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- 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