Relaxation of regularity for the Westervelt equation by nonlinear damping with applications in acoustic-acoustic and elastic-acoustic coupling

Rainer Brunnhuber; Barbara Kaltenbacher; Petronela Radu

doi:10.3934/eect.2014.3.595

Article Contents

2014, Volume 3, Issue 4: 595-626. Doi: 10.3934/eect.2014.3.595

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Relaxation of regularity for the Westervelt equation by nonlinear damping with applications in acoustic-acoustic and elastic-acoustic coupling

1.
Institut für Mathematik, Universität Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt am Wörthersee
2.
Department of Mathematics, University of Nebraska-Lincoln, Avery Hall 239, Lincoln, NE 68588

Received: November 30, 2013

Revised: February 28, 2014

Published: November 2014

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Abstract

In this paper we show local (and partially global) in time existence for the Westervelt equation with several versions of nonlinear damping. This enables us to prove well-posedness with spatially varying $L_\infty$-coefficients, which includes the situation of interface coupling between linear and nonlinear acoustics as well as between linear elasticity and nonlinear acoustics, as relevant, e.g., in high intensity focused ultrasound (HIFU) applications.

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Mathematics Subject Classification: Primary: 35L05; Secondary: 35L20.

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