Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems.
Global solution to the Cauchy problem of nonlinear thermodiffusion in a solid body
We consider the initial-value problem for a nonlinear hyperbolic-parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove global (in time) existence and uniqueness of the solution to the initial-value problem for this nonlinear system. The global existence is proved using time decay estimates for the solution of the associated linearized problem. Next, we prove an energy estimate...