On \({(W_2^1(\mathbb R)\cap W_\infty^1(\mathbb R))}\)-solutions of the equation \({u_{tt}=(a(u)u_x)_x+f(x,t)}\)

DOI10.1016/j.jmaa.2014.06.059zbMath1297.35143OpenAlexW2211652168MaRDI QIDQ401101

Peter E. Zhidkov

Publication date: 26 August 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.06.059

zbMATH Keywords

existence and uniquenessquasi-linear wave equationinterval of existencelife-time of the smooth solutionlife-time of the weak solution

Mathematics Subject Classification ID

Weak solutions to PDEs (35D30) Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Second-order quasilinear hyperbolic equations (35L72)

Cites Work

• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• On weak solutions of the initial value problem for the equation \(u_{tt}=a(x,t)u_{xx}+f(t,x,u,u_t,u_x)\)
• Delayed singularity formation in solution of nonlinear wave equations in higher dimensions
• On nonlinear partial differential equations with two independent variables
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