Email this article Nonlocal Tricomi boundary value problem for a mixed-type differential-difference equation
- Authors: Zarubin A.N.1
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Affiliations:
- Orel State University named after I. S. Turgenev
- Issue: Vol 25, No 1 (2021)
- Pages: 35-50
- Section: Differential Equations and Mathematical Physics
- URL: https://bakhtiniada.ru/1991-8615/article/view/60180
- DOI: https://doi.org/10.14498/vsgtu1835
- ID: 60180
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Abstract
We investigate the Tricomi boundary value problem for a differential-difference leading-lagging equation of mixed type with non-Carleman deviations in all in all arguments of the required function. A reduction is applied to a mixed-type equation without deviations. Symmetric pairwise commutative matrices of the coefficients of the equation are used. The theorems of uniqueness and existence are proved. The problem is unambiguously solvable.
About the authors
Alexandr Nikolaevich Zarubin
Orel State University named after I. S. Turgenev
Author for correspondence.
Email: matdiff@yandex.ru
ORCID iD: 0000-0002-0611-5752
SPIN-code: 9296-6666
Scopus Author ID: 10046147800
http://www.mathnet.ru/rus/person44134
Dr. Phys. & Math. Sci., Professor; Head of Dept.; Dept. of Mathematical Analysis and Differential Equations
95, Komsomolskaya st., Orel, 119192, Russian FederationReferences
- Sharkovsky A. N., Maistrenko Yu. L., Romanenko E. Yu Difference Equations and Their Applications, Mathematics and Its Applications, vol. 250. Dordrecht, Kluwer Academic Publ., 1993, xii+358 pp. https://doi.org/10.1007/978-94-011-1763-0.
- Onanov G. G., Skubachevskii A. L. Differential equations with displaced arguments in stationary problems in the mechanics of a deformable body, Sov. Appl. Mech., 1979, vol. 15, no. 5, pp. 391–397. https://doi.org/10.1007/BF01074069.
- Samarskii A. A. Some problems of the theory of differential equations, Differ. Uravn., 1980, vol. 16, no. 11, pp. 1925–1935 (In Russian).
- Maslov V. P. Operatornye metody [Operational Methods]. Moscow, Nauka, 1973, 544 pp. (In Russian)
- Gantsev Sh., Bakhtizin R. N., Frants M. V., Gantsev K. Sh. Tumor growth and mathematical modeling of system processes, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2019, vol. 23, no. 1, pp. 131–151 (In Russian). https://doi.org/10.14498/vsgtu1661.
- Bellman R. Introduction to matrix analysis, Society for Industrial and Applied Mathematics, vol. 19. Philadelphia, PA, 1997, xxviii+403 pp.
- Frankl F. I. Izbrannye trudy po gazovoi dinamike [Selected Works on Gas Dynamics]. Moscow, Nauka, 1973, 712 pp. (In Russian)
- Zarubin A. N. Uravneniia smeshannogo tipa s zapazdyvaiushchim argumentom [Mixed-Type Equations with Retarded Argument]. Orel, Orel State Univ., 1997, 225 pp. (In Russian)
- Gakhov F. D. Boundary Value Problems, International Series of Monographs in Pure and Applied Mathematics, vol. 85. Oxford, Pergamon Press, 1966, xix+564 pp. https://doi.org/10.1016/C2013-0-01739-2.
- Flaysher N. M. A new closed-form solution method for some classes of singular integral equations with a regular part, Rev. Roum. Math. Pures Appl., 1965, vol. 10, no. 5, pp. 615–620 (In Russian).
- Baburin Yu. S. On the singularization of singular integral equations, In: Differentsial’nye uravneniia [Differential Equations], Issue 10. Ryazan, 1977, pp. 14–24 (In Russian).
- Krasnov M. L. Integral’nye uravneniia: vvedenie v teoriiu [Integral Equations. Introduction to the Theory]. Moscow, Nauka, 1975, 303 pp. (In Russian)
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