LIFESPAN OF SOLUTIONS FOR TWO SPACE DIMENSIONAL WAVE EQUATIONS WITH CUBIC NONLINEARITY

DOI10.1081/PDE-100001753zbMath0982.35069MaRDI QIDQ2747911

Soichiro Katayama

Publication date: 26 March 2002

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

zbMATH Keywords

estimates from below of the lifespan

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (11)

Global existence for semilinear wave equations with the critical blow-up term in high dimensions ⋮ The small data solutions of general 3-D quasilinear wave equations. II. ⋮ The Small Data Solutions of General 3D Quasilinear Wave Equations. I ⋮ Small data solutions of 2-D quasilinear wave equations under null conditions ⋮ Combined effects of two nonlinearities in lifespan of small solutions to semi-linear wave equations ⋮ Global existence and blow up for systems of nonlinear wave equations related to the weak null condition ⋮ Lifespan of classical solutions to semilinear Neumann-wave equations ⋮ Almost global solutions of semilinear wave equations with the critical exponent in high dimensions ⋮ The combined effect in one space dimension beyond the general theory for nonlinear wave equations ⋮ Global and almost global existence for general quasilinear wave equations in two space dimensions ⋮ Blow Up for Some Semilinear Wave Equations in Multi-space Dimensions

Cites Work

• Global existence of small solutions to nonlinear evolution equations
• Existence in the large for \(cmu=F(u)\) in two space dimensions
• Global existence for systems of nonlinear wave equations in two space dimensions
• Global existence for systems of nonlinear wave equations in two space dimensions. II
• Lifespan of solutions of semilinear wave equations in two space dimensions
• Almost global existence to nonlinear wave equations 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
• Long‐time behaviour of solutions of a system of nonlinear wave equations
• Existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data
• Global existence for nonlinear wave equations
• Remarks on the global sobolev inequalities in the minkowski space Rⁿ⁺¹
• Global, small amplitude solutions to nonlinear evolution equations
• On the lifespan of solutions of nonlinear wave equations with small initial data

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