Well Posedness and Polynomial Decay of Solution to the Initial‐Boundary Value Problem in Thermodiffusion for a Solid Body

ABSTRACT In this paper, we consider a hyperbolic‐parabolic system of equations describing the thermodiffusion in a solid body. The theory of thermodiffusion is a combination of the theory of heat conduction and diffusion with the theory of elasticity. In this work, we establish the well‐posedness of an initial‐boundary value problem for a system describing this phenomenon, using the semigroup theory. Moreover, we prove a polynomial decay of solutions satisfying certain properties.