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Boundary behavior of the fast diffusion equation


Author: Y. C. Kwong
Journal: Trans. Amer. Math. Soc. 322 (1990), 263-283
MSC: Primary 35K55; Secondary 35B99
DOI: https://doi.org/10.1090/S0002-9947-1990-1008697-0
MathSciNet review: 1008697
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Abstract: The fast diffusion equation $ \Delta {\upsilon ^m} = {\upsilon _t}$, $ 0 < m < 1$, is a degenerate nonlinear parabolic equation of which the existence of a unique continuous weak solution has been established. In this paper we are going to obtain a Lipschitz growth rate of the solution at the boundary of $ \Omega $ and estimate that in terms of the various data.


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DOI: https://doi.org/10.1090/S0002-9947-1990-1008697-0
Article copyright: © Copyright 1990 American Mathematical Society

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