Asymptotic behavior of solutions to reaction-diffusion equations with dynamic boundary conditions and irregular data (Q1727269)

Summary: This paper is concerned with the asymptotic behavior of solutions to reaction-diffusion equations with dynamic boundary conditions as well as \(L^1\)-initial data and forcing terms. We first prove the existence and uniqueness of an entropy solution by smoothing approximations. Then we consider the large-time behavior of the solution. The existence of a global attractor for the solution semigroup is obtained in \(L^1(\overline{\Omega}, d \nu)\). This extends the corresponding results in the literatures.