\(L_p-L_q\)-theory for a quasilinear non-isothermal westervelt equation

DOI10.1007/s00245-023-09987-zOpenAlexW4363675805MaRDI QIDQ2701090

Mathias Wilke

Publication date: 27 April 2023

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.09630

zbMATH Keywords

exponential stabilityoptimal regularityparabolic-hyperbolic systemquasilinear parabolic systemPennes bioheat equationnon-isothermal Westervelt equationpropagation of sound in fluids

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for systems of nonlinear higher-order PDEs (35G61)

Cites Work

• Unnamed Item
• The Westervelt equation with a causal propagation operator coupled to the bioheat equation
• Boundary observability and stabilization for Westervelt type wave equations without interior damping
• Optimal regularity and long-time behavior of solutions for the Westervelt equation
• Global existence and exponential decay rates for the Westervelt equation
• On convergence of solutions to equilibria for quasilinear parabolic problems
• Boundary optimal control of the Westervelt and the Kuznetsov equations
• The Westervelt-Pennes model of nonlinear thermoacoustics: global solvability and asymptotic behavior
• Well-posedness of the Westervelt and the Kuznetsov equation with nonhomogeneous Neumann boundary conditions
• Optimal \(L^{p}\)- \(L^{q}\)-estimates for parabolic boundary value problems with inhomogeneous data
• Well-posedness and longtime behavior for the Westervelt equation with absorbing boundary conditions of order zero
• Moving Interfaces and Quasilinear Parabolic Evolution Equations
• Analysis in Banach Spaces
• Nonlinear analytic semiflows
• Sharp embedding results for spaces of smooth functions with power weights
• Linear and Quasilinear Parabolic Problems
• Fundamental models in nonlinear acoustics part I. Analytical comparison
• The Inviscid Limit of Third-Order Linear and Nonlinear Acoustic Equations
• Solvability and maximal regularity of parabolic evolution equations with coefficients continuous in time

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