On the solvability of nonlocal problem with generalized operators M. Saigo for Bitsadze–Lykov equation

• Main Authors: Anna V. Tarasenko, Irina P. Egorova
• Format: Article
• Language: English
• Published: Samara State Technical University 2014-12-01
• Series: Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
• Subjects: boundary value problem; generalized operator of fractional integro-differentiation; integral equation with Cauchy kernel
• Online Access: http://mi.mathnet.ru/eng/vsgtu1363

A nonlocal boundary value problem for the equation of moisture transfer was studied in the field, which is the union of two characteristic triangles. The novelty of the formulation of the problem lies in the fact that the boundary conditions include operators of generalized of fractional integro-differentiation in the sense of M. Saigo. The uniqueness of the solution of the problem was proved using the extremum principle for hyperbolic equations. Properties of operators of generalized fractional integro-differentiation in the sense of M. Saigo were used in the proof. Existence of a solution is equivalent reduced to the solvability of a characteristic singular integral equation with Cauchy kernel for which the smoothness of the right-hand side was studied.