Time periodic solutions of porous medium equation

✍ Scribed by Jun Zhou; Chunlai Mu

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 213 KB
• Volume: 33
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1307

✦ Synopsis

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 ak 1 , where k 1 is the first eigenvalue of the operator -D 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.