文章基本信息

标题：Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation
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作者：A. S. Berdyshev ; E. T. Karimov ; N. Akhtaeva 等
期刊名称：International Journal of Differential Equations
印刷版ISSN：1687-9643
电子版ISSN：1687-9651
出版年度：2011
卷号：2011
DOI：10.1155/2011/268465
出版社：Hindawi Publishing Corporation
摘要：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.