Investigation and solving of initial-boundary value problem including fourth order PDE by contour integral and asymptotic methods
عنوان مقاله: Investigation and solving of initial-boundary value problem including fourth order PDE by contour integral and asymptotic methods
شناسه ملی مقاله: JR_JMMO-11-2_003
منتشر شده در در سال 1402
شناسه ملی مقاله: JR_JMMO-11-2_003
منتشر شده در در سال 1402
مشخصات نویسندگان مقاله:
Reza Danaei - Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Mohammad Jahanshahi - Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
خلاصه مقاله:
Reza Danaei - Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Mohammad Jahanshahi - Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
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.
کلمات کلیدی: Asymptotic method, Laplace line, Eigenvalues, Contour integral
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1995559/