Cauchy–Goursat Problem for One-Dimensional Semilinear Wave Equations

DOI10.1080/03605300902768966zbMath1167.35413OpenAlexW2061130490MaRDI QIDQ5321925

O. M. Dzhokhadze

Publication date: 16 July 2009

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

Full work available at URL: https://doi.org/10.1080/03605300902768966

zbMATH Keywords

blow-upnonlinear wave equationsglobal and local solvabilityinitial-characteristic problempositive power nonlinearity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Critical exponents in context of PDEs (35B33) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (11)

On the solvability of a boundary value problem for nonlinear wave equations in angular domains ⋮ The second Darboux problem for the wave equation with integral nonlinearity ⋮ The first Darboux problem for wave equations with nonlinear dissipative term ⋮ A Numerical Algorithm for a Coupled Hyperbolic Boundary Value Problem ⋮ A numerical method for solving a Goursat-Cauchy boundary value problem ⋮ The Cauchy-Darboux problem for the one-dimensional wave equation with power nonlinearity ⋮ Unnamed Item ⋮ Existence of global solution and traveling wave of the modified short-wave equation ⋮ Second Darboux problem for the wave equation with a power-law nonlinearity ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

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• Nonexistence of global solutions to semilinear wave equations in high dimensions
• The global Goursat problem on \(R\times S^ 1\)
• Blow-up of solutions of nonlinear wave equations in three space dimensions
• Blow up for nonlinear dissipative wave equations in \(\mathbb R^n\)
• On existence and nonexistence of global solutions of Cauchy-Goursat problem for nonlinear wave equations
• The global Goursat problem and scattering for nonlinear wave equations
• Biow-up of solutions of some nonlinear hyperbolic equations
• Weighted Strichartz estimates and global existence for semilinear wave equations

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