Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations - Assanova, A.T.; Tokmurzin, Zh.S. (KU publ., 2020)
A semi-periodic initial boundary-value problem for a fourth-order system of partial differential equations is considered. Using the method of functional parametrization, an additional parameter is carried out and the studied problem is reduced to the equivalent semi-periodic problem for a system of integro-differential equations of hyperbolic type second order with functional parameters and integral relations. An interrelation between the semi-periodic problem for the system of integro-differential equations of hyperbolic type and a family of Cauchy problems for a system of ordinary differential equations is established. Algorithms for finding of solutions to an equivalent problem are constructed and their convergence is proved. Sufficient conditions of a unique solvability to the semi-periodic initial boundary value problem for the fourth-order system of partial differential equations are obtained.
Төрітінші ретті дербес туындылы дифференциалдық теңдеулер үшін жартылайпериодты бастапқы есепті шешудің функционалдық параметрлеу әдісі
Методы функциональной параметризации решения полупериодической начальной задачи для дифференциальных уравнений в частных производных четвертого порядка
Keywords: semi-periodic initial boundary-value problem; fourth-order system of partial differential equations; the method of functional parametrization; semi-periodic problem; system of integro-differential equations of hyperbolic type second order; family of Cauchy problems; algorithm; unique solvability