A boundary value problem with adjointing condition of integral type for mixed parabolic - hyperbolic equations with non-characteristic line type change.
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Keywords:
mixed parabolo-hyperbolic equation, conditions of adjointing, integral equation,Abstract
In work questions of unique solvability of one local problem with integrated conditions of adjointing on the line of change of type for mixed parabolo-hyperbolic equation of the second order are studied. Under certain restrictions on the data of the problem we prove the existence and uniqueness of solutions of the problem.References
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[3] Капустин Н.Ю., Моисеев Е.И. О спектральных задачах со спектральным параметром в граничном условии. // Дифференц. уравнения. - 1997. - Т.33. No 1. – С.115-119.
[4] Eshmatov B.E., Karimov E.T. Boundary value problems with continuous and special gluing conditions for parabolic–hyperbolic type equations. // Cent.Eur. J. Math.-2007.- Vol.5, No 4. – P.741–750.
[5] Berdyshev A.S., Rakhmatullaeva N.A. Nonlocal Problems with Special Gluing for a Parabolic- Hyperbolic Equation // Proceedings of the 6th International ISAAC Congress "Further Progress in Analysis". Ankara, Turkey, 13-18 August 2007. – P. 727-734.
[6] Berdyshev A.S., Karimov E.T., Akhtaeva N.S. Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation // International Journal of Differential Equations 2011, Volume 2011, Article ID 268465, 10 pages. doi:10.1155/2011/268465.
[7] Berdyshev A.S., Cabada A., Karimov E.T. On a non-local boundary problem for a parabolic-hyperbolic equation involving a Riemann-Liouville fractional differential operator // Nonlinear analysis: Theory, Methods and Applications (NATMA).-2012.Vol.75. No 6. – P.3268-3273.
[2] Джураев Т.Д., Сопуев А., Мамажонов М. Краевые задачи для уравнений параболо-гиперболического типа. // Ташкент: Фан. – 1986. – 220 с.
[3] Капустин Н.Ю., Моисеев Е.И. О спектральных задачах со спектральным параметром в граничном условии. // Дифференц. уравнения. - 1997. - Т.33. No 1. – С.115-119.
[4] Eshmatov B.E., Karimov E.T. Boundary value problems with continuous and special gluing conditions for parabolic–hyperbolic type equations. // Cent.Eur. J. Math.-2007.- Vol.5, No 4. – P.741–750.
[5] Berdyshev A.S., Rakhmatullaeva N.A. Nonlocal Problems with Special Gluing for a Parabolic- Hyperbolic Equation // Proceedings of the 6th International ISAAC Congress "Further Progress in Analysis". Ankara, Turkey, 13-18 August 2007. – P. 727-734.
[6] Berdyshev A.S., Karimov E.T., Akhtaeva N.S. Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation // International Journal of Differential Equations 2011, Volume 2011, Article ID 268465, 10 pages. doi:10.1155/2011/268465.
[7] Berdyshev A.S., Cabada A., Karimov E.T. On a non-local boundary problem for a parabolic-hyperbolic equation involving a Riemann-Liouville fractional differential operator // Nonlinear analysis: Theory, Methods and Applications (NATMA).-2012.Vol.75. No 6. – P.3268-3273.
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Akhtaeva, N. S., & Karimov, E. T. (2013). A boundary value problem with adjointing condition of integral type for mixed parabolic - hyperbolic equations with non-characteristic line type change. Journal of Mathematics, Mechanics and Computer Science, 77(2), 64–70. Retrieved from https://bm.kaznu.kz/index.php/kaznu/article/view/96
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Mechanics, Mathematics, Computer Science
