On Hopf type functional derivative equations for \(\square{} u+cu+bu^ 2+au^ 3 = 0\) on \(\Omega{} \times{} R\). I: Existence of solutions

DOI10.1016/0022-247X(90)90093-UzbMath0739.35042OpenAlexW2057977020MaRDI QIDQ1173638

Atsushi Inoue

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0022-247x(90)90093-u

zbMATH Keywords

nonlinear Klein-Gordon equationmany-time Hopf equation

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Higher-order nonlinear hyperbolic equations (35L75) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Cites Work

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• Strong and classical solutions of the Hopf equation - an example of functional derivative equation of second order
• A certain functional derivative equation corresponding to \(\square u+cu+bu^ 2+au^ 3=g\) on \(R^{d+1}\)
• An invariant measure for the equation \(u_{tt}-u_{xx}+u^ 3=0\)
• Some examples exhibiting the procedures of renormalization and gauge fixing. - Schwinger-Dyson equations of first order
• L'equation de Hopf, les solutions statistiques, les moments correspondants aux systèmes des équations paraboliques quasilineaires
• Sur \(\square u+u^3=f\) dans un domaine noncylindrique
• Statistical study of Navier-Stokes equations. I
• Statistical study of Navier-Stokes equations. II
• On the solvability of the Cauchy problem for the Hopf equation corresponding to a nonlinear hyperbolic equation
• SOME MATHEMATICAL PROBLEMS OF STATISTICAL HYROMECHANICS
• MEASURES ON LINEAR TOPOLOGICAL SPACES

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