Study on phase transition problems with nonlinear control devices

点击翻译按钮获取中文摘要

We study a phase transition model of the phase field type in a vessel, which is a coupled system of two second order parabolic PDEs for temerature field and non-conserved order parameter. In order to control the order parameter, we use some control devices on the fixed boundary, which are usually described as a nonlinear boundary condition. In our study, we consider the dynamic boundary condition which includes the time derivative of temperature field on the fixed boundary. The purpose of our study is to prove existence and uniqueness of solutions with the well-posedness ina sufficiently large space. Our approach to this problem is based on the abstract theory of nonlinear evolution equations governd by time-dependent subdifferentials in Hilbert spaces.