Local well-posedness of a quasilinear wave equation

DOI10.1080/00036811.2015.1089236zbMath1350.35128OpenAlexW2291209308WikidataQ58270887 ScholiaQ58270887MaRDI QIDQ2825400

Roland Schnaubelt, Hannes Gerner, Willy Dörfler

Publication date: 7 October 2016

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2015.1089236

zbMATH Keywords

nonlinear opticsKerr nonlinearityKato's methodKato stability

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Second-order quasilinear hyperbolic equations (35L72)

Related Items (10)

Parabolic Approximation of Quasilinear Wave Equations with Applications in Nonlinear Acoustics ⋮ Trigonometric integrators for quasilinear wave equations ⋮ Exponential Integrators for Quasilinear Wave-Type Equations ⋮ On the global controllability of the \(1\)-D Boussinesq equation ⋮ A high-order discontinuous Galerkin method for nonlinear sound waves ⋮ One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations ⋮ Weakly Nonlinear Geometric Optics for the Westervelt Equation and Recovery of the Nonlinearity ⋮ Error analysis of implicit Euler methods for quasilinear hyperbolic evolution equations ⋮ Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type ⋮ The Jordan–Moore–Gibson–Thompson Equation: Well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time

Cites Work

• Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles
• Sharp local well-posedness results for the nonlinear wave equation
• Semigroups of linear operators and applications to partial differential equations
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• On global smooth solutions to the initial-boundary value problem for quasilinear wave equations in exterior domains
• Global smooth solutions for the quasilinear wave equation with boundary dissipation
• Time-Domain Simulations of the Nonlinear Maxwell Equations Using Operator-Exponential Methods

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