An alternative proof of global existence for nonlinear wave equations in an exterior domain

DOI10.2969/jmsj/06041135zbMath1156.35058arXiv0706.1833OpenAlexW2963662087MaRDI QIDQ998937

Hideo Kubo, Soichiro Katayama

Publication date: 30 January 2009

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.1833

zbMATH Keywords

exterior domainobstaclenull conditionsystem of quasilinear wave equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Higher-order hyperbolic systems (35L55) Initial-boundary value problems for higher-order hyperbolic equations (35L35)

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Cites Work

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• On the global existence of classical solutions of second order fully nonlinear hyperbolic equations with first order dissipation in the exterior domain
• Singularities and energy decay in acoustical scattering
• Hyperbolic trapped rays and global existence of quasilinear wave equations
• Global solvability for systems of nonlinear wave equations with multiple speeds in two dimensions.
• Global small amplitude solutions to systems of nonlinear wave equations with multiple speeds
• On a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain
• Decay of solutions of the wave equation in the exterior of several convex bodies
• Decay of solutions of the wave equation in the exterior of two convex obstacles
• Global existence of classical solutions to systems of wave equations with critical nonlinearity in three space dimensions
• Global existence for a quasilinear wave equation outside of star-shaped domains
• The global existence theorem for quasi-linear wave equations with multiple speeds
• Resonance-type behaviour in a system of nonlinear wave equations
• Global existence of small solutions to quadratic nonlinear wave equations in an exterior domain
• Global and almost-global existence for systems of nonlinear wave equations with different propagation speeds.
• Global existence of null-form wave equations in exterior domains
• Global Existence for Systems of Nonlinear Wave Equations in 3D with Multiple Speeds
• Decay Estimates of a Tangential Derivative to the Light Cone for the Wave Equation and Their Application
• Existence of a global solution to a semi–linear wave equation with slowly decreasing initial data in three space dimensions
• Global solutions of nonlinear hyperbolic equations for small initial data
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Blow-up for quasi-linear wave equations in three space dimensions
• Global Existence of Solutions to Multiple Speed Systems of Quasilinear Wave Equations in Exterior Domains
• Global Existence of Solutions to Some Exterior Radial Quasilinear Cauchy- Dirichlet Problems
• Solutions of the wave equation with localized energy