On a Class of Coupled Variational Formulations for a Nonlinear Parabolic Equation

In this paper, we apply the coupling of finite element and boundary integral methods to solve the initial boundary value problem for nonlinear parabolic equations in the plane, which consists of a nonlinear parabolic equation in divergence form in a bounded inner region, and the heat equation in the corresponding unbounded exterior region. The variational formulation of the coupled problem is given. The well-posedness of the variational problem is proved.