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2011 Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation
A. S. Berdyshev, E. T. Karimov, N. Akhtaeva
Int. J. Differ. Equ. 2011(SI1): 1-10 (2011). DOI: 10.1155/2011/268465

Abstract

Analogs of the Tricomi and the Gellerstedt problems with integral gluing conditions for mixed parabolic-hyperbolic equation with parameter have been considered. The considered mixed-type equation consists of fractional diffusion and telegraph equation. The Tricomi problem is equivalently reduced to the second-kind Volterra integral equation, which is uniquely solvable. The uniqueness of the Gellerstedt problem is proven by energy integrals' method and the existence by reducing it to the ordinary differential equations. The method of Green functions and properties of integral-differential operators have been used.

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A. S. Berdyshev. E. T. Karimov. N. Akhtaeva. "Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation." Int. J. Differ. Equ. 2011 (SI1) 1 - 10, 2011. https://doi.org/10.1155/2011/268465

Information

Received: 18 May 2011; Accepted: 11 October 2011; Published: 2011
First available in Project Euclid: 26 January 2017

zbMATH: 1235.35201
MathSciNet: MR2862686
Digital Object Identifier: 10.1155/2011/268465

Rights: Copyright © 2011 Hindawi

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