On the unique solvability of a nonlocal boundary value problem with data on intersecting lines for systems of hyperbolic equations

A Family of Two-Point Boundary Value Problems for Loaded Differential Equations

“…For the solution of the family of two-point boundary value problems (1), ( 2), the Dzhumabaev parameterization method [25] is used, which was developed to study the boundary problem for systems of ordinary differential equations. Based on this method, the criteria were established for the unique correct solvability of various boundary value problems for differential equations [25]- [28], [10] and nonlocal problems for a system of hyperbolic equations with mixed derivatives [29]- [31]. Note that the families of two-point boundary value problems (1), ( 2) are non-Fredholm problems [32].…”

“…A solution to the problem ( 26)-( 29) is a pair (26), boundary conditions (27), initial conditions on splitting lines (28), and continuity condition (29).…”

“…. , m + 1, we have constructed the unique solution to the problem ( 26)-(29), the system of pairs ( v * (t, [x]), μ * (t)), where the vector-function μ * (t) is presentable in form (41), and the components of the vector-function v * (t, x) are presentable in form (47), satisfying the system of equations (26) and conditions ( 27)- (29).…”

On the Initial-Boundary Value Problem for System of the Partial Differential Equations of Fourth Order

“…We will investigate the questions of existence and uniqueness of the classical solutions to the initial-boundary value problem for system of the partial differential equations of fourth order (1)--(5) and the approaches of constructing its approximate solutions. For this goals, we applied the method of introduction additional functional parameters proposed in [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] for solving of various nonlocal problems for systems of hyperbolic equations with mixed derivatives. Considered problem is provided to nonlocal problem for the system of hyperbolic equations of second order including additional functions and integral relation.…”

Goursat problem for two-dimensional second-order hyperbolic operator-differential equations with variable domains

“…The existence and uniqueness of classical solutions of a second-order hyperbolic partial differential equation with degenerating mixed derivative under Goursat conditions and without boundary conditions were studied in [6]. A nonlocal boundary value problem was solved in [7] for hyperbolic equations whose coefficients are square matrices of scalar functions.…”