Asymptotic bounds of solutions for a periodic doubly degenerate parabolic equation

作者：Sun, Jiebao^*; Yin, Jingxue; Wang, Yifu

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(6): 2415-2424.

DOI：10.1016/j.na.2010.11.044

• Periodic solutions
• Doubly degenerate
• Moser iteration
• Asymptotic bounds

This paper is concerned with a doubly degenerate parabolic equation with logistic periodic sources. We are interested in the discussion of the asymptotic behavior of solutions of the initial-boundary value problem. In this paper, we first establish the existence of non-trivial nonnegative periodic solutions by a monotonicity method. Then by using the Moser iterative method, we obtain an a priori upper bound of the nonnegative periodic solutions, by means of which we show the existence of the maximum periodic solution and asymptotic bounds of the nonnegative solutions of the initial-boundary value problem. We also prove that the support of the non-trivial nonnegative periodic solution is independent of time.

• 出版日期2011-3-15
• 单位北京理工大学; 哈尔滨工业大学; 华南师范大学