Global solution of the Cauchy problem in nonlinear thermodi.usion in solid body

Abstract

We prove a theorem about global existence (in time) of the solution to the initial-value problem for a nonlinear hyperbolic parabolic system of coupled partial differential equation of second order describing the process of thermodiffusion in solid body. The corresponding global existence theorems has been proved using the Lp - Lq time decay estimates for the solution of the associated linearized problem. Next, we proved the energy estimate in the Sobolev space with constant independent of time. Such an energy estimate allows us to apply the standard (continuation argument and to continue the local solution to one de.ned for all t ∈ 〈0, ∞)).