Straburzyński, Jan On the existence, uniqueness and continuous dependence of solutions of the Goursat problem for differential-functional equations of hyperbolic type. (English) Zbl 0661.35061 Differential equations and optimal control, Proc. 5th Reg. Sci. Sess., Zagań/Pol. 1985, Sect.: Differential equations, 93-100 (1986). [For the entire collection see Zbl 0634.00011.] The problem of existence, uniqueness and continuous dependence of initial data and the right-hand side for the Goursat problem of the hyperbolic differential equations of \(Z_{xy}==f(x,y,z,z_ x,z_ y)\) is studied. It is assumed that f satisfies Carathéodory type conditions. Reviewer: M.Bartušek MSC: 35L70 Second-order nonlinear hyperbolic equations 35L20 Initial-boundary value problems for second-order hyperbolic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:hyperbolic equations; existence; uniqueness; continuous dependence; Goursat problem; Carathéodory type conditions Citations:Zbl 0634.00011 PDFBibTeX XML