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Applications of the Hille-Yosida theorem to the linearized equations of coupled sound and heat flow. (English) Zbl 1428.35104
Summary: This paper deals with the initial-value problem for the linearized equations of coupled sound and heat flow, in a bounded domain $$\Omega$$ in $$\mathbb{R}^N$$, 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 A. Carasso [Math. Comput. 29, 447–463 (1975; Zbl 0311.65061)]. Moreover, regularity of solutions is established.

MSC:
 35G46 Initial-boundary value problems for systems of linear higher-order PDEs 47D06 One-parameter semigroups and linear evolution equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 35B65 Smoothness and regularity of solutions to PDEs
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