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On the Cattabriga problem for airy equation in domains with curvilinear boundaries

Popiołek J.

Demonstratio Mathematica

1998

Vol. 31, nr 3

643-655

This paper is concerned with the Cattabriga problem for Airy equation (a linear version of the Korteweg - de Vries equation) in domains with curvilinear boundaries. Applying the potential method we shall reduce the problem considered to a system of Volterra integral equations and then prove the existence of a solution of this system.This paper is related to the previous investigations, where the said problem has been solved in rectangular domains.