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Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters. (English) Zbl 1418.35277

The authors investigate an acoustic problem of 1D wave propagation through a discontinuous medium. The problem is reduced to an equivalent one which is governed by a dissipative wave equation with distributional dissipation. For non-smooth data the problem has a very weak solution, a concept introduced by C. Garetto and the second author [J. Differ. Equations 258, No. 12, 4324–4347 (2015; Zbl 1328.35261)]. In addition, the authors derive properties of the solution and illustrate the theoretical results with numerical simulations for a particular piecewise continuous medium.

MSC:

35L81 Singular hyperbolic equations
35D99 Generalized solutions to partial differential equations
35L15 Initial value problems for second-order hyperbolic equations
76Q05 Hydro- and aero-acoustics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction

Citations:

Zbl 1328.35261
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References:

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