JournalszaaVol. 23 , No. 1DOI 10.4171/zaa/1185

A Class of Partial Integro-Differential Equations with Correlation-Convolution Integral I

  • Lothar von Wolfersdorf

    Technische Universität, Freiberg, Germany
A Class of Partial Integro-Differential Equations with Correlation-Convolution Integral I cover

Abstract

By means of the iteration method with weighted norms existence and uniqueness theorems are proved for three classes of nonlinear integral equations and first order integro-differential equations in two variables. The quadratic non-linearity is given by the correlation-convolution integral. Existence and uniqueness of the solutions are shown in Lebesgue spaces with mixed norms in rectangle and strip.