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

Citation: Ayaka Matsubara, Tomomi Yokota. Applications of the Hille-Yosida theorem to the linearized equations of coupled sound and heat flow. AIMS Mathematics, 2016, 1(3): 165-177. doi: 10.3934/Math.2016.3.165

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.

 

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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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