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- Title
Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics.
- Authors
Fritz, Marvin; Nikolić, Vanja; Wohlmuth, Barbara
- 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.
- Subjects
NONLINEAR wave equations; DIRICHLET problem; BOUNDARY value problems; FIXED point theory; FINITE element method; NONLINEAR acoustics
- Publication
Mathematical Models & Methods in Applied Sciences, 2018, Vol 28, Issue 13, p2557
- ISSN
0218-2025
- Publication type
Article
- DOI
10.1142/S0218202518500550