Initial value problems for nonlinear wave equations

DOI10.1080/03605308808820547zbMath0662.35071OpenAlexW2026873625MaRDI QIDQ3811052

Yunmei Chen, Ta-Tsien Li

Publication date: 1988

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308808820547

zbMATH Keywords

global convergenceenergy estimatesexistencesmall parameterCauchy problemapproximate solutionsdecay estimatesBanach fixed point theoremsemilinearunique global classical solution

Mathematics Subject Classification ID

Related Items (26)

A remark on global smooth solutions for quasilinear wave equations ⋮ The small data solutions of general 3-D quasilinear wave equations. II. ⋮ Initial boundary-value problems for quasilinear wave equations with dissipation in an exterior domain ⋮ Life-span of classical solutions to two dimensional fully nonlinear wave equations ⋮ The Small Data Solutions of General 3D Quasilinear Wave Equations. I ⋮ Long time classical solutions of a nonlinear wave equation ⋮ The fully non-linear Cauchy problem with small data ⋮ Lifespan of classical solutions to one dimensional fully nonlinear wave equations with time-dependent damping ⋮ Lifespan of classical solutions to semilinear Neumann-wave equations ⋮ Life-Span of Classical Solutions to a Semilinear Wave Equation with Time-Dependent Damping ⋮ The rescaling method for some quasilinear wave equations with the divergence forms of the nonlinearity ⋮ Global solutions to systems of quasilinear wave equations with low regularity data and applications ⋮ Global smooth solutions of 3-D null-form wave equations in exterior domains with Neumann boundary conditions ⋮ Life-span of classical solutions to one dimensional initial-boundary value problems for general quasilinear wave equations ⋮ Slowly decaying solutions for semilinear wave equations in odd space dimensions ⋮ Global and almost global existence for general quasilinear wave equations in two space dimensions ⋮ Blowup time and blowup mechanism of small data solutions to general 2-D quasilinear wave equations ⋮ Global existence and asymptotic behavior of the fractional chemotaxis system with signal-dependent sensitivity ⋮ Life-span of classical solutions to one dimensional initial-boundary value problems for general quasilinear wave equations with Robin boundary conditions ⋮ Global Oscillatory Waves for Second Order Quasilinear Wave Equations ⋮ The rescaling method for some critical quasilinear wave equations with the divergence form of the nonlinearity ⋮ Weighted decay estimates for the wave equation ⋮ Life-span of classical solutions to fully nonlinear wave equations—II ⋮ The lower bounds of life span of classical solutions to one-dimensional initial-Neumann boundary value problems for general quasilinear wave equations ⋮ Global small data smooth solutions of 2-D null-form wave equations with non-compactly supported initial data ⋮ On the blowup and lifespan of smooth solutions to a class of 2-D nonlinear wave equations with small initial data

Cites Work

• Global existence of small solutions to nonlinear evolution equations
• Long-time behavior of solutions to nonlinear evolution equations
• On the classical solvability of the Cauchy problem for nonlinear wave equations with small initial values and the asymptotic behavior of the solutions
• Global solutions of nonlinear hyperbolic equations for small initial data
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Global existence for nonlinear wave equations
• Global, small amplitude solutions to nonlinear evolution equations

This page was built for publication: Initial value problems for nonlinear wave equations