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arXiv · 1806.05227

Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics

Marvin Fritz·Vanja Nikolić·Barbara Wohlmuth
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Abstract

We study the Blackstock equation which models the propagation of nonlinear sound waves through dissipative fluids. Global well-posedness of the model with homogeneous Dirichlet boundary conditions is shown for small initial data. To this end, we employ a fixed-point technique coupled with well-posedness results for a linearized model and appropriate energy estimates. Furthermore, we obtain exponential decay for the energy of the solution. We present additionally a finite element-based method for solving the Blackstock equation and illustrate the behavior of solutions through several numerical experiments.

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Marvin Fritz, Vanja Nikolić, Barbara Wohlmuth. 2018-07-04. Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics. https://doi.org/10.1142/s0218202518500550

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