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Danaei, Reza, Jahanshahi, Mohammad. (1402). Investigation and solving of initial-boundary value problem including fourth order PDE by contour integral and asymptotic methods. فیزیولوژی و بیوتکنولوژی آبزیان, 11(2), 245-255. doi: 10.22124/jmm.2023.23209.2069
Reza Danaei; Mohammad Jahanshahi. "Investigation and solving of initial-boundary value problem including fourth order PDE by contour integral and asymptotic methods". فیزیولوژی و بیوتکنولوژی آبزیان, 11, 2, 1402, 245-255. doi: 10.22124/jmm.2023.23209.2069
Danaei, Reza, Jahanshahi, Mohammad. (1402). 'Investigation and solving of initial-boundary value problem including fourth order PDE by contour integral and asymptotic methods', فیزیولوژی و بیوتکنولوژی آبزیان, 11(2), pp. 245-255. doi: 10.22124/jmm.2023.23209.2069
Danaei, Reza, Jahanshahi, Mohammad. Investigation and solving of initial-boundary value problem including fourth order PDE by contour integral and asymptotic methods. فیزیولوژی و بیوتکنولوژی آبزیان, 1402; 11(2): 245-255. doi: 10.22124/jmm.2023.23209.2069

Investigation and solving of initial-boundary value problem including fourth order PDE by contour integral and asymptotic methods

Journal of Mathematical Modeling
مقاله 3، دوره 11، شماره 2، مهر 2023، صفحه 245-255    اصل مقاله (293.62 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2023.23209.2069
نویسندگان
Reza Danaei* ؛ Mohammad Jahanshahi
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
چکیده
In this paper, we consider a fourth order mixed partial differential equation with some initial and boundary conditions which is unsolvable by classical methods such as Fourier, Fourier-Bircove and Laplace Transformation methods. For this problem we will apply the contour integral and asymptotic methods. The convergence of the appeared integrals, existence and uniqueness of solution, satisfying the solution and holding the given initial  and boundary conditions are stablished by complex analysis theory and related contour integrals. Finally, the form of analytic  and approximate solutions are given due to different cases of eigenvalues distributions in the  complex plane.
کلیدواژه‌ها
Asymptotic method؛ ‎Laplace ‎line؛ ‎Eigenvalues؛ ‎ ‎Contour ‎integral
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