On weak solutions of the initial value problem for the equation \(u_{tt}=a(x,t)u_{xx}+f(t,x,u,u_t,u_x)\)

DOI10.1016/J.NA.2012.11.014zbMath1259.35142OpenAlexW185623458MaRDI QIDQ1934994

Peter E. Zhidkov

Publication date: 30 January 2013

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.11.014

zbMATH Keywords

global solutionlocal well-posednessone space dimensionnon-autonomous equationstrict hyperbolicity

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Initial value problems for second-order hyperbolic equations (35L15) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Second-order semilinear hyperbolic equations (35L71)

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

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