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Explicit solutions of Cauchy problems for degenerate hyperbolic equations with Transmutations methods | ||
| Journal of Mathematics and Modeling in Finance | ||
| مقاله 12، دوره 2، شماره 1، مهر 2022، صفحه 209-247 اصل مقاله (282.51 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2022.14574 | ||
| نویسندگان | ||
| Mahdieh Aminian Shahrokhabadi1؛ Hossein Azari* 2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran. | ||
| 2Shahid Beheshti University | ||
| چکیده | ||
| This article's primary goal is to compute an explicit transmutation-based solution to a degenerate hyperbolic equation of second order in terms of time. To reduce a new problem to a problem that has already been solved, or at the very least to a smaller problem, is a standard mathematics strategy known as the transmutations method. similar to utilizing heat equations to solve wave equations. Using transmutation methods, we solve this problem using the well-known Kolmogorov equation. We present the solution of wave equations using transmutation methods and show that it is equivalent to the solution obtained by applying the Fourier transform in order to support our methodology. | ||
| کلیدواژهها | ||
| Degenerate Partial Differential Equations؛ Transmutation Methods؛ Kolmogorov Equation؛ Inverse Laplace Transform؛ Laplace Transform | ||
| مراجع | ||
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[1] A. Kolmogorov, Zu lige Bewegungen. (Zur Theorie der Brownschen Bewegung), Ann. of Math., .ser., 35, pp. 116-117, 1934. [2] L.R. Bragg and J.W. Dettman, Related problems in partial differential equations, Bull Amer. Math. Soc., vol. 74, pp.375-378, 1968. [3] L.R. Bragg and J.W. Dettman, Related problems in partial differential equations and their applications, SIAM J. Appl. Math, vol. 16, pp. 459-467, 1968. [4] L.R. Bragg and J.W. Dettman, An operator calculus for related partial differential equations, J. Math. Anal. Appl., vol. 22, pp. 261-271, 1968. [5] R. Hersh, The Method of Transmutations, in Partial Differential Equations and Related Topics, Springer, 1974. [6] L.R. Bragg and J.W. Dettman, A Class of Related Dirichlet and Initial Value Problems, Proceedings of the American Mathematical Society, vol. 21, no. 1, pp. 5056, 1969. [7] N. Garofalo, Partial Differential Equations Text Book, Preprint. [8] Y. Kannai, Off diagonal short time asymptotics for fundamental solution of diffusion equation, Communications in Partial Equations, pp. 781-830, 1977. [9] V. Kiryakova, Transmutatin method for solving hyper{Bessel differential equations based on the Poisson Dimovski transformation, Fractinal Calculus and Applied Analysis (FCAA), vol.11. [10] Fadhel Almalki and Vladimir V. Kisil, Solving the Schrodinger equation by reduction to a rst order differential operator through a coherent states transform, Physics Letters A, vol. 384, no. 16, 2020. [11] S.I. ROSENCRANS, Diffusion Transforms, Journal of Differential Equations, vol. 13, pp. 457-467, 1972. [12] A.V. Balakrishnan,Abstract Cauchy Problems of the elliptic type, Bull. Amer. Math. Soc.,vol. 64, pp. 290-291,1958. [13] R. Griego and R. Hersh,Theory of Random Evolutions with Applications to Partial Differential Equations, Transactions of the American Mathematical Society, vol. 156, pp. 405-418,1971. [14] A.H. Zemanian,Distribution theory and transform analysis, McGraw{Hill"1965. [15] E.C. Titchmarsh, The Theory of functions, 2nd ed, New York: Oxford Univ. Press, 1939. [16] A. Friedman, Partial differential equations of parabolic type, Englewood Clifs: Prentice{Hall1964. " [17] F. Anceschi, On the Kolmogorov equation: regularity theory and applications, Universit`a degli Studi di Modena e Reggio Emilia: Thesis, 2021. [18] Y. Zhu, Velocity averaging and Holder regularity for kinetic Fokker-Planck equations with general transport operators and rough coefficients, preprint arXiv:2010.03867, 2020. [19] C. Imbert and L. Silvestre, The schauder estimate for kinetic integral equations. | ||
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