×

zbMATH — the first resource for mathematics

Local solutions for a nonlinear unilateral problem. (English) Zbl 0613.35051
It is proved existence and uniqueness of local solutions for a unilateral problem for the operators \[ u\mapsto \partial^ 2u/\partial t^ 2+M(\int_{\Omega}| \nabla u(x,t)|^ 2 dx)(-\Delta u) \] \[ u\to \partial^ 2u/\partial t^ 2+M(\int_{\Omega}| \nabla u(x,t)|^ 2 dx+\int_{\Omega}u^ 2(x,t)dx)(-\Delta u+u), \] where the real function \(\lambda\mapsto M(\lambda)\) defined for all \(\lambda\geq 0\) is continuously differentiable and \(M(\lambda)\geq m_ 0>0\) for all \(\lambda\geq 0\).
Reviewer: V.Kostova

MSC:
35L85 Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
PDF BibTeX XML Cite