Existence and uniform decay of solutions of a parabolic-hyperbolic equation with nonlinear boundary damping and boundary source term
A mixed problem for a linear hyperbolic-parabolic equation is considered when on the part of the lateral boundary the Dirichlet condition is given and on the rest of the boundary a nonlinear damping and a source term are given. Under the assumption that the damping is predominant over the source, the existence of global solutions is proved. If the damping and the source terms have the same growth, the uniform decay of strong and weak solutions is proved.
scientific article; zbMATH DE number 1893853