Existence and uniqueness of periodic solutions for a quasilinear parabolic problem

Abstract

We are concerned with the existence and uniqueness of the nonnegative periodic weak solution to a quasilinear parabolic problem of degenerate type, which describes a mathematical model in petroleum engineering. The existence of periodic solutions is established by means of the Schauder fixed point Theorem applied to the Poincaré map. Instead, the uniqueness of the periodic solution is proved under the assumption that $b(\varphi^-1)$ is Hölder continuous of order 1/2, adapting a technique utilized in the study of nonlinear hyperbolic equations.