On the Neumann problem for some linear hyperbolic-parabolic coupled systems with coefficients in Sobolev spaces

Abstract

We prove a unique existence theorem of classical solutions to some Neumann problem of linear hyperbolic-parabolic coupled systems with coefficients in Sobolev spaces and energy estimates are also obtained. This paper gives a preparation for solving some nonlinear hyperbolic-parabolic coupled system with Neumann boundary condition.