Bulletin KRASEC. Phys. & Math. Sci. 2016. V. 13. no. 2. pp. 25-30. ISSN 2313-0156

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DOI: 10.18454/2313-0156-2016-13-2-25-30

MSC 65M32

GELLERSTEDT PROBLEM FOR A PARABOLIC-HYPERBOLIC EQUATION WITH
DEGENERACY OF TYPE AND ORDER

Z. S. Madrakhimova

Institute of Мathematics, National University of Uzbekistan, Tashkent, 100125, Academgorodok, Do’rmon yo’li, 29 str.
E-mail: zilolaxonmadrahimova@gmail.com

This paper deals with the formulation and study of a boundary value Gellerstedt problem for parabolic-hyperbolic equation with degeneracy of type and order within a domain which is equivalently reduced to integral equations.

Key words: Gellerstedt problem, parabolic-hyperbolic equation, degeneracy of type and order, integral equations, integral-differential operator of fractional order, modified Cauchy problem.

References

  1. Smirnov M. M. Uravneniya smeshannogo tipa [Mixed equations]. Moscow. Nauka. 1985. 304 p.
    2. Tersenov S. A. Pervaya kraevaya zadacha dlya uravneniya parabolo-giperbolicheskogo tipa s menyayushchimisya napravleniem vremeni [First boundary value problem for parabolic-hyperbolic equation with time changing direction]. Novosibirsk. 1978. 52 p.
    3. Vatson G. N. Teoriya Besselevykh funktsiy [Theory of Bessel functions]. vol. 1. 1949. Мoscow. Izdatel’stvo inostrannoy literatury. 798 p.
    4. Mikhlin S. G. Lektsii po lineynymi integral’nymi uravneniyam [Lectures on linear integral equations]. Moscow. Fizmatgiz.1959. 224 p.

For citation: Madrakhimova Z. S. Gellerstedt problem for a parabolic-hyperbolic equation with degeneracy of type and order. Bulletin KRASEC. Physical and Mathematical Sciences 2016, vol. 13, no 2, 25-30. DOI: 10.18454/2313-0156-2016-13-2-25-30.

Original article submitted: 01.06.2016

Mad

   Madrakhimova Zilolakhon Sodikzhonovna – Ph.D.(Phys & Math), Senior Lecturer, Department of differential equations and mathematical physics, National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Republic of Uzbekistan.

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