Existence of solutions to some non‐linear thermoelastic systems with viscosity
Karl Heinz Hoffmann, Antoni Żochowski · Mathematical Methods in the Applied Sciences · 1992
Abstract In this paper a non‐linear system of equations magnified image in a one‐dimensional domain is considered, where both the viscosity, v, and R are positive. The existence of solutions in the case of Neumann boundary conditions for θ and a polynomial form of p(θ, ϵ) is proved. When θ satisfies the Dirichlet boundary condition, the existence of solutions is obtained under additional assumptions limiting the growth of p(θ, ϵ) with respect to θ. In both cases the uniqueness of the solutions is also established.