On the existence of time-periodic solutions of some non-linear evolution equation^†

^†This work was supported under Grant NRC A-3004 by the National Research Counci of Canada

Abstract

In this paper we study time-periodic solutions for Dirichlet type boundary value problems for some non-linear evolution equations with time-periodic forcing term. Our equations include semi-linear elliptic terms as well as non-linear damping terms, the form of which is suggested from the "friction term" in the system of equations for water waves in one-dimen¬sional form, Under suitable assumptions on both the elliptic terms and the damping terms, we shall give a proof of the existence of weak, time-periodic solutions, using Faedo-Galerkin method, in the context of Sobolev spaces

^†This work was supported under Grant NRC A-3004 by the National Research Counci of Canada

^†This work was supported under Grant NRC A-3004 by the National Research Counci of Canada

Notes

^†This work was supported under Grant NRC A-3004 by the National Research Counci of Canada