A remark on nonexistence of global solutions to quasi-linear hyperbolic and parabolic equations

DOI10.1016/S0893-9659(02)80010-6zbMath1002.35011OpenAlexW2092682405MaRDI QIDQ1609516

D. Erdem, Varga K. Kalantarov

Publication date: 15 August 2002

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(02)80010-6

zbMATH Keywords

sufficient conditions for global nonexistence

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for second-order hyperbolic equations (35L20) Initial-boundary value problems for second-order parabolic equations (35K20) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Second-order nonlinear hyperbolic equations (35L70)

Related Items (1)

Blow up, exponential growth of solution for a reaction-diffusion equation with multiple nonlinearities

Cites Work

• Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics
• Nonexistence of global weak solutions for classes of nonlinear wave and parabolic equations
• The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types
• Blow-up of solutions to quasilinear parabolic equations
• Existence and nonexistence of solutions for \(u_ t=\text{div}(|\nabla u|^{p-2}\nabla u)+f(\nabla u,u,x,t)\)
• Das Rand-Anfangswertproblem für quasilineare Wellengleichungen in Sobolevräumen niedriger Ordnung.

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