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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

Citations:

Zbl 0311.65061
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References:

[1] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext. Springer, New York, 2011. · Zbl 1220.46002
[2] A, Coupled sound and heat flow and the method of least squares, Math. Comp, 29, 447-463 (1975) · Zbl 0311.65061
[3] F. Harlow and A. Amsden, Fluid Dynamics, LASL Monograph LA 4700, Los Alamos Scientific Laboratories, Los Alamos, N. M., 1971.
[4] R. D. Richtmyer and K.W. Morton, Difference Methods for Initial-Value Problems, Second edition, Interscience, New York, 1967. · Zbl 0155.47502
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