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

DOI10.1142/S0218202518500550zbMath1421.35217arXiv1806.05227WikidataQ129378278 ScholiaQ129378278MaRDI QIDQ4630544

Marvin Fritz, Vanja Nikolić, Barbara I. Wohlmuth

Publication date: 27 March 2019

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.05227

zbMATH Keywords

exponential decayenergy decayfixed-point techniquepropagation of nonlinear sound waves

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Hydro- and aero-acoustics (76Q05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (6)

Asymptotic behaviors for Blackstock's model of thermoviscous flow ⋮ Time-weighted estimates for the Blackstock equation in nonlinear ultrasonics ⋮ Nonlinear acoustic equations of fractional higher order at the singular limit ⋮ Self-adaptive absorbing boundary conditions for quasilinear acoustic wave propagation ⋮ The Jordan–Moore–Gibson–Thompson Equation: Well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time ⋮ A Priori Error Estimates for the Finite Element Approximation of Westervelt's Quasi-linear Acoustic Wave Equation

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