Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Equations of Mathematical Physics

On a boundary value problem for a system of hyperbolic equations with the wave operator and a singular coefficient of lower derivatives

R. R. Rayanova

Samara State Technical University, Samara, 443100, Russia

Abstract: The boundary value problem with data given on the parallel characteristics for the system of hyperbolic equations with the wave operator and the singular matrix coefficient at the lower derivative is considered in the characteristic square. This system of differential equations in the characteristic coordinates can be reduced to the system of Euler–Poisson–Darboux equations. Using the known solution of Cauchy problem with data given on the singularity line of matrix coefficient, we reduce the problem to the Carleman system of integral equations.The explicit solution of the considered boundary value problem is constructed using the results of previous research on the solvability of the systems of generalized Abel integral equations, made by the author.

Keywords: Riemann–Liouville fractional calculation, matrix functions, integral-differentional operators of matrix order, system of generalized Abel integral equations, Carleman integral equation.

UDC: 517.968.78

MSC: 35L80

Original article submitted 29/X/2012
revision submitted – 27/I/2013

DOI: 10.14498/vsgtu1129

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