Time periodic solutions of porous medium equation
Jun Xing Zhou, Chunlai Mu · Mathematical Methods in the Applied Sciences · 2010
In this article, we study the time periodic solutions to the following porous medium equation under the homogeneous Dirichlet boundary condition: The existence of nontrivial nonnegative solution is established provided that 0≤α }{\lambda}_1$\end{document}, where λ1 is the first eigenvalue of the operator −Δ under the homogeneous Dirichlet boundary condition. We also show that the support of these solutions is independent of time by providing a priori estimates for their upper bounds using Moser iteration. Further, we establish the attractivity of maximal periodic solution using the monotonicity method. Copyright © 2010 John Wiley & Sons, Ltd.