Lower bounds for the life span of solutions of nonlinear wave equations in higher dimensions

DOI10.1016/0362-546X(84)90003-8zbMath0545.35061OpenAlexW1996614987MaRDI QIDQ3334313

Gustavo Ponce

Publication date: 1984

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(84)90003-8

zbMATH Keywords

perturbationKlein-Gordon equationquasilinear equationsnonlinear wave equationunique global classical solutionKlainerman condition

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15)

Cites Work

• Unnamed Item
• Global existence of small solutions to nonlinear evolution equations
• \(L^p-L^q\) estimates for the Klein-Gordon equation
• Nonlinear scattering theory at low energy
• Long-time behavior of solutions to nonlinear evolution equations
• \(L^ p\)-decay rates for homogeneous wave-equations
• Formation of singularities for wave equations including the nonlinear vibrating string
• Blow-up for quasi-linear wave equations in three space dimensions
• Delayed singularity formation in solution of nonlinear wave equations in higher dimensions
• Global existence for nonlinear wave equations
• Global, small amplitude solutions to nonlinear evolution equations
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Convolutions with Kernels Having Singularities on a Sphere

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