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1. Complicated asymptotic behavior of solutions for porous medium equation in unbounded space.

Author

Wang, Liangwei, Yin, Jingxue, and Zhou, Yong

Subjects
*PARTIAL differential equations, *DIFFERENTIAL equations, *BIHARMONIC equations, *BIHARMONIC functions, *CAUCHY problem
Abstract

In this paper, we find that the unbounded spaces Y σ ( R N ) ( 0 < σ < 2 m − 1 ) can provide the work spaces where complicated asymptotic behavior appears in the solutions of the Cauchy problem of the porous medium equation. To overcome the difficulties caused by the nonlinearity of the equation and the unbounded solutions, we establish the propagation estimates, the growth estimates and the weighted L 1 – L ∞ estimates for the solutions. [ABSTRACT FROM AUTHOR]

Published
2018
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