MATHEMATICS

The Gellerstedt problem for advanced-retarded mixed type equation with variable deviation

A. N. Zarubin, E. Chaplygina

Orel State University named after I. S. Turgenev

Abstract: We study the Gellerstedt problem for a mixed type equation with the Lavrent?ev-Bitsadze operator in the main part and a variable deviation of the argument. The equation general solution has been built up. Uniqueness theorem is proved without any restrictions on the amount of deviation. We have found explicitly integral representations of solutions in the domains of ellipticity and hyperbolicity.

Keywords: mixed type equation, Cauchy problem, Dirichlet problem, differential equation, the Gellerstedt problem.

UDC: 517.956

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