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Aminian Shahrokhabadi, Mahdieh, Azari, Hossein. (1401). Explicit solutions of Cauchy problems for degenerate hyperbolic equations with Transmutations methods. سامانه مدیریت نشریات علمی, 2(1), 209-247. doi: 10.22054/jmmf.2022.14574
Mahdieh Aminian Shahrokhabadi; Hossein Azari. "Explicit solutions of Cauchy problems for degenerate hyperbolic equations with Transmutations methods". سامانه مدیریت نشریات علمی, 2, 1, 1401, 209-247. doi: 10.22054/jmmf.2022.14574
Aminian Shahrokhabadi, Mahdieh, Azari, Hossein. (1401). 'Explicit solutions of Cauchy problems for degenerate hyperbolic equations with Transmutations methods', سامانه مدیریت نشریات علمی, 2(1), pp. 209-247. doi: 10.22054/jmmf.2022.14574
Aminian Shahrokhabadi, Mahdieh, Azari, Hossein. Explicit solutions of Cauchy problems for degenerate hyperbolic equations with Transmutations methods. سامانه مدیریت نشریات علمی, 1401; 2(1): 209-247. doi: 10.22054/jmmf.2022.14574

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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