A Global Existence Theorem for Semilinear Wave Equations with Data of Non Compact Support in Two Space Dimensions

DOI10.1080/03605309208820909zbMath0815.35074OpenAlexW2068600423MaRDI QIDQ4033777

Kimitoshi Tsutaya

Publication date: 16 May 1993

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

Full work available at URL: https://doi.org/10.1080/03605309208820909

zbMATH Keywords

semilinear wave equationsglobal existence resultsdata of noncompact supportlower bounds for the life span

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70)

Related Items (10)

Lower bounds of the life span of classical solutions to a system of semilinear wave equations in two space dimensions ⋮ Blow-up for semilinear wave equations in four or five space dimensions ⋮ Small data blow-up for the wave equation with a time-dependent scale invariant damping and a cubic convolution for slowly decaying initial data ⋮ Slowly decaying solutions for semilinear wave equations in odd space dimensions ⋮ Critical blowup for systems of semilinear wave equations in low space dimensions ⋮ Scattering Theory for Semilinear Wave Equations with Small Data in Two Space Dimensions ⋮ Blow-up theorem for semilinear wave equations with non-zero initial position ⋮ On the critical decay for the wave equation with a cubic convolution in 3D ⋮ Scattering theory for semilinear wave equations with small data in two space dimensions ⋮ Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential

Cites Work

• Unnamed Item
• Unnamed Item
• Finite-time blow-up for solutions of nonlinear wave equations
• Existence in the large for \(cmu=F(u)\) in two space dimensions
• The lifespan of classical solutions to nonlinear wave equations in two space dimensions
• Blow-up of solutions of nonlinear wave equations in three space dimensions
• Existence of a global solution to a semi-linear wave equation with initial data of non-compact support in low space dimensions
• The equation u_tt − Δu = |u|^p for the critical value of p
• Existence of a global solution to a semi–linear wave equation with slowly decreasing initial data in three space dimensions
• Long‐time behaviour of solutions of a system of nonlinear wave equations

This page was built for publication: A Global Existence Theorem for Semilinear Wave Equations with Data of Non Compact Support in Two Space Dimensions