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Nonlinear Acoustics: Blackstock–Crighton Equations with a Periodic Forcing Term

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Abstract

Blackstock–Crighton equations describe the motion of a viscous, heat-conducting, compressible fluid. They are used as models for acoustic wave propagation in a medium in which both nonlinear and dissipative effects are taken into account. In this article, a mathematical analysis of the Blackstock–Crighton equations with a time-periodic forcing term is carried out. For time-periodic data sufficiently restricted in size it is shown that a time-periodic solution of the same period always exists. This implies that the dissipative effects are sufficient to avoid resonance within the Blackstock–Crighton models. The equations are considered in a bounded domain with both non-homogeneous Dirichlet and Neumann boundary values. Existence of a solution is obtained via a fixed-point argument based on appropriate a priori estimates for the linearized equations.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    Aday Celik & Mads Kyed

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  1. Aday Celik
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  2. Mads Kyed
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Correspondence to Mads Kyed.

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Communicated by E. Feireisl

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Celik, A., Kyed, M. Nonlinear Acoustics: Blackstock–Crighton Equations with a Periodic Forcing Term. J. Math. Fluid Mech. 21, 45 (2019). https://doi.org/10.1007/s00021-019-0451-4

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  • DOI: https://doi.org/10.1007/s00021-019-0451-4

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