AIMS Mathematics, 2016, 1(3): 165-177. doi: 10.3934/Math.2016.3.165

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

Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

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.
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References

1. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext. Springer, New York, 2011.

2. A. Carasso, Coupled sound and heat flow and the method of least squares, Math. Comp. 29 (1975),447–463.

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.

Copyright Info: © 2016, Tomomi Yokota, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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