Matsubara, Ayaka; Yokota, Tomomi Applications of the Hille-Yosida theorem to the linearized equations of coupled sound and heat flow. (English) Zbl 1428.35104 AIMS Math. 1, No. 3, 165-177 (2016). 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. Cited in 2 Documents 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 Keywords:monotone operators; homogeneous Dirichlet boundary conditions Citations:Zbl 0311.65061 PDFBibTeX XMLCite \textit{A. Matsubara} and \textit{T. Yokota}, AIMS Math. 1, No. 3, 165--177 (2016; Zbl 1428.35104) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.