Открытый доступ
Доступ предоставлен
Только для подписчиков
Том 238, № 3 (2019)
- Год: 2019
- Статей: 13
- URL: https://journal-vniispk.ru/1072-3374/issue/view/14998
Article
One Approach to the Solution of a Nonlocal Problem for Systems of Hyperbolic Equations with Integral Conditions
Аннотация
We consider a nonlocal problem with integral conditions for a system of hyperbolic equations with two independent variables. We study the solvability of the considered problem and construct algorithms aimed at finding its approximate solutions by introducing additional functional parameters. The investigated problem is reduced to an equivalent problem that consists of the Goursat problem for a system of hyperbolic equations with parameters and a boundary-value problem with integral condition for a system of ordinary differential equations for the introduced parameters. We propose algorithms for finding approximate solutions of the problem based on the algorithms used for the solution of the equivalent problem and prove their convergence to the exact solution.
189-206
Nonclassical Symmetries of a System of Nonlinear Reaction-Diffusion Equations
Аннотация
We study the conditional symmetry of a system of nonlinear reaction-diffusion equations and establish the existence of operators of conditional symmetry for systems of nonlinear reaction-diffusion equations with any number of independent variables and find these operators in the explicit form. The exact solutions of nonlinear reaction-diffusion equations with exponential nonlinearity are constructed.
207-214
215-223
Bifurcation of Solutions of the Boundary-Value Problem for Systems of Integrodifferential Equations with Degenerate Kernel
Аннотация
We establish sufficient conditions for the existence of solutions of a weakly perturbed linear boundary-value problems for a system of integrodifferential equations. We also establish conditions for the existence and uniqueness of solutions of problems of this kind and propose an iterative procedure for the construction of the required solutions.
224-235
Synchronization Analysis for a Class of Genetic Oscillator Networks
Аннотация
We consider a synchronization problem for genetic oscillator networks. The genetic oscillators are modeled as nonlinear systems of the Lur’e type. Simple and verifiable synchronization conditions are presented for genetic oscillator networks by using the theory of absolute stability and the matrix theory. A network composed of coupled Goodwin models is used as an example of numerical simulation to verify the efficiency of the theoretical method.
236-247
Weakly Perturbed Boundary-Value Problems for the Fredholm Integral Equations with Degenerate Kernel in Banach Spaces
Аннотация
We consider weakly perturbed boundary-value problems for the Fredholm integral equations with degenerate kernel in Banach spaces and establish the conditions of bifurcation from the point ε = 0 for the solutions of weakly perturbed boundary-value problems for Fredholm integral equations with degenerate kernel in Banach spaces. A convergent iterative procedure is proposed for finding the solutions in the form of series \( {\sum}_{i=-1}^{+\infty }{\varepsilon}^i{z}_i(t) \) in powers of ε.
248-262
On the Exponential Stability of a Trivial Torus for One Class of Nonlinear Impulsive Systems
Аннотация
We prove the exponential stability of a trivial torus for a class of nonlinear extensions of dynamical systems on a torus. The obtained results can be applied to the study of stability of toroidal sets for a certain class of impulsive dynamical systems.
263-270
Asymptotic Expansion of the Solution of a Linear Parabolic Boundary-Value Problem in a Thin Starlike Joint
Аннотация
We consider a linear parabolic boundary-value problem in a thin 3D starlike joint that consists of a finite number of thin curvilinear cylinders connected through a domain (node) with diameter O(ε). We develop a procedure for the construction of the complete asymptotic expansion of the solution as ε → 0, i.e., in the case where the starlike joint is transformed into a graph. By using the method of matching of the asymptotic series, we deduce the limit problem (ε = 0) on a graph with the corresponding Kirchhoff-type conjugation conditions at the vertex. We also prove asymptotic estimates, which enable us to trace the influence of the geometric shape of the node and the physical processes running in the node on the global asymptotic behavior of the solution.
271-291
292-301
302-315
316-332
Matrix Differential-Algebraic Boundary-Value Problem with Pulsed Action
Аннотация
We establish necessary and sufficient conditions for the existence of solutions of a linear matrix boundaryvalue problem for a system of matrix differential-algebraic equations with pulsed action. We also construct a generalized Green operator of linear boundary conditions for a system of matrix differentialalgebraic equations with pulse action. To solve the matrix differential-algebraic boundary problem with pulsed action, we use the original conditions of solvability and the structure of the general solution of the linear matrix equation.
333-343
Correction
344-344