Abstract:
A nonlinear heat equation with a piston on the boundary is discussed, where the piston term is a time-periodic function. In the past several decades, the study of time periodic solutions for all kinds nonlinear diffusion equations with nonlinear sources have achieved fruitful results, but there are very few results for the study of the diffusion equations with time periodic boundary. The linear, sublinear and superlinear cases are studied respectively, and it is shown that for the sublinear case and linear case, there always exists time periodic solution for any piston; while for the superlinear case, time periodic solution exists when the boundary value is small.