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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the regularity properties for solutions of the Cauchy problem for the porous media equation


Author: Kazuya Hayasida
Journal: Proc. Amer. Math. Soc. 107 (1989), 107-112
MSC: Primary 35K55; Secondary 35K65, 76S05
MathSciNet review: 948150
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Abstract: We consider the Cauchy problem for the equation $ {\partial _t}u = \Delta {u^m}$ in $ {R^N} \times (0,T)$. We assume that $ 1 < m < 3N/(3N - 2)$ and the initial data $ {u_0}$ is in $ C_0^1({R^N})$ and $ {u_0} \geq 0$ in $ {R^N}$. Then we prove that the second derivatives of $ {u^m}$ with respect to the space-variable are in $ {L^2}({R^N} \times (0,T))$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0948150-0
PII: S 0002-9939(1989)0948150-0
Keywords: Porous media, initial data
Article copyright: © Copyright 1989 American Mathematical Society