Zeitschrift für Analysis und ihre Anwendungen 23 (2004), No. 2, 313--333
Copyright Heldermann Verlag 2004
A Class of Partial Integro-Differential Equations with Correlation-Convolution Integral II
Lothar von Wolfersdorf
Fakultät f. Mathematik und Informatik, Technische Universität, 09596 Freiberg, Germany
wolfersdorf@math.tu-freiberg.de
Three classes of nonlinear integral equations and first order integro-differential equations in two variables are dealt with where the quadratic nonlinearity is given by the correlation-convolution integral. In the case of the quarter plane the equations are reduced to boundary value problems for holomorphic functions which can be solved in closed form. In this way existence and constructive formulas for the solutions to the equations are derived.
Keywords: Nonlinear integral equations, nonlinear partial integro-differential equations, correlation-convolution integral, boundary value problem for holomorphic functions.
MSC: 45G10, 45K05; 44A35, 30E25
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