On the solvability of the Cauchy problem for the Hopf equation corresponding to a nonlinear hyperbolic equation

DOI10.1090/TRANS2/118/08zbMath0495.35056OpenAlexW4242090694MaRDI QIDQ3958843

Mark I. Vishik, Alexander I. Komech

Publication date: 1982

Published in: American Mathematical Society Translations: Series 2 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/trans2/118/08

zbMATH Keywords

Cauchy problemexistence theoremGalerkin approximationgrowth conditionsstatistical solutionHopf equationnontrivial stationary solutionArzela theorem

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Second-order nonlinear hyperbolic equations (35L70) Theoretical approximation in context of PDEs (35A35) PDEs with randomness, stochastic partial differential equations (35R60) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (2)

A certain functional derivative equation corresponding to \(\square u+cu+bu^ 2+au^ 3=g\) on \(R^{d+1}\) ⋮ On Hopf type functional derivative equations for \(\square{} u+cu+bu^ 2+au^ 3 = 0\) on \(\Omega{} \times{} R\). I: Existence of solutions

This page was built for publication: On the solvability of the Cauchy problem for the Hopf equation corresponding to a nonlinear hyperbolic equation