Ein Randwertproblem für eine nichtlineare Gleichung gemischtenTyps im

  • Andreas Müller-Rettkowski

    Karlsruhe Institute of Technology (KIT), Germany

Abstract

A boundary value problem for the equation , is studied in a simply connected bounded domain of . Here denotes a linear second order differential operator which is elliptic, parabolic or hyperbolic if or , respectively. The boundary of 0 is formed by a non-characteristic and by two characteristic surfaces. The boundary value problem to be solved is to find a solution of the equation in 0 which assumes zero data on the non-characteristic and on one of the characteristic boundary surfaces. It is proved that this problem has a generalized solution belonging to and to a Sobolew space with weight. Using apriori estimates the solubility of a sequence of approximate problems is shown whose solutions turn out to converge towards a solution of the boundary value problem in question.

Cite this article

Andreas Müller-Rettkowski, Ein Randwertproblem für eine nichtlineare Gleichung gemischtenTyps im . Z. Anal. Anwend. 3 (1984), no. 5, pp. 413–423

DOI 10.4171/ZAA/118