Nonexistence of global solutions of a nonlinear hyperbolic system

DOI10.1090/S0002-9947-97-01841-2zbMath0960.35063OpenAlexW1505830214MaRDI QIDQ3127274

Keng Deng

Publication date: 8 April 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-01841-2

zbMATH Keywords

blow-up singularitiessemilinear hyperbolic equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Analyticity in context of PDEs (35A20)

Related Items (16)

Profile of blow-up solution to hyperbolic system with nonlocal term ⋮ Existence and asymptotic behavior of radially symmetric solutions to a semilinear hyperbolic system in odd space dimensions ⋮ Unnamed Item ⋮ Global existence for a coupled wave system related to the Strauss conjecture ⋮ Lower bounds of the life span of classical solutions to a system of semilinear wave equations in two space dimensions ⋮ On the critical curve for systems of hyperbolic inequalities in an exterior domain of the half-space ⋮ Critical exponent for parabolic system with time-weighted sources in bounded domain ⋮ Global nonexistence results for a class of hyperbolic systems ⋮ Critical blowup for systems of semilinear wave equations in low space dimensions ⋮ The role of critical exponents in blow-up theorems: The sequel ⋮ Blow-up solutions of some nonlinear hyperbolic systems ⋮ Blow-up phenomena of semilinear wave equations and their weakly coupled systems ⋮ Global existence and nonexistence of solutions for a system of nonlinear damped wave equations ⋮ Small data blowup for systems of semilinear wave equations with different propagation speeds in three space dimensions ⋮ Global existence and blow-up of solutions for a system of fractional wave equations ⋮ Blow-up for the ω-heat equation with Dirichlet boundary conditions and a reaction term on graphs

Cites Work

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• A Fujita type global existence-global nonexistence theorem for a weakly coupled system of reaction-diffusion equations
• Blow-up of solutions of nonlinear wave equations in three space dimensions
• Approximation of nonlinear evolution systems
• The equation u_tt − Δu = |u|^p for the critical value of p
• Biow-up of solutions of some nonlinear hyperbolic equations
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)

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