An Existence Theorem for a Quasilinear Hyperbolic Boundary Value Problem Solved by Semidiscretization in Time

Abstract

By the use of Rothe’s method there is proved the existence of a solution of a quasilinear hyperbolic boundary value problem. On the coefficients and the right-hand side only integrability is assumed. With such weak assumptions there exists a subsequence of Rothe approximations that converges (in a weak sense) to a solution of the problem.