Threshold Behavior for Nonlinear Wave Equations

DOI10.2991/jnmp.2001.8.s.7zbMath0980.35109OpenAlexW4251537652MaRDI QIDQ2732450

Piotr Bizoń

Publication date: 29 October 2001

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2991/jnmp.2001.8.s.7

zbMATH Keywords

Klein-Gordon equationthreshold of singularity

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Analyticity in context of PDEs (35A20) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (10)

Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions ⋮ High order variable mesh off-step discretization for the solution of 1-D non-linear hyperbolic equation ⋮ On blowup for the supercritical quadratic wave equation ⋮ Stable blowup for the cubic wave equation in higher dimensions ⋮ The blow-up rate for a non-scaling invariant semilinear wave equations in higher dimensions ⋮ Approximation of nonlinear wave equations with nonstandard anisotropic growth conditions ⋮ The blow-up rate for a non-scaling invariant semilinear wave equations ⋮ On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations ⋮ The blow-up rate for strongly perturbed semilinear wave equations in the conformal regime without a radial assumption ⋮ Solution to the semilinear wave equation with a pyramid-shaped blow-up surface

Cites Work

• Blow-up of solutions of nonlinear wave equations in three space dimensions
• The formation of black holes and singularities in spherically symmetric gravitational collapse
• Long‐time behaviour of solutions of a system of nonlinear wave equations
• Weak solutions and development of singularities of the SU(2) σ‐model
• Bounded variation solutions of the spherically symmetric einstein‐scalar field equations
• Dispersion and collapse of wave maps
• Global existence of harmonic maps in minkowski space
• Critical phenomena in gravitational collapse
• Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere

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