Applications of the Hille-Yosida theorem to the linearized equations of coupled sound and heat flow

Abstract

This paper deals with the initial-value problem for the linearized equations of coupled sound and heat flow, in a bounded domain Ω in RN, with homogeneous Dirichlet boundary conditions. Existence and uniqueness of solutions to the problem are established by using the Hille-Yosida theorem. This paper gives a simpler proof than one by Carasso (1975). Moreover, regularity of solutions is established.

Keywords

• coupled sound and heat flow|monotone operators|the Hille-Yosida theorem|existence|uniqueness|regularity of solutions