V. G. Sorokin (Ishlinsky Institute for Problems in Mechanics) :
Articles:
517.929+517.95 Analytical solutions of nonlinear transport equations with delay
Sorokin V. G. (Ishlinsky Institute for Problems in Mechanics)
doi: 10.18698/2309-3684-2024-3-140167
Nonlinear transport equations with constant delay are considered. The introduction provides a brief overview of publications that study transport mathematical models with delay and develop numerical methods for solving the corresponding problems. The main sections of the article describe more than forty transport equations with constant delay and various transfer coefficients, which allow exact analytical solutions. The kinetic functions of all considered equations contain free parameters or arbitrary functions. Additive, multiplicative, generalized, and functional separable solutions, as well as traveling-wave and self-similar solutions are obtained. Many solutions are expressed in terms of elementary functions. For some types of equations, theorems on the “multipli-cation” of solutions are formulated. The described equations and their solutions can be used to evaluate the accuracy of numerical methods for integrating the corresponding nonlinear transport problems with delay.
Сорокин В.Г. Аналитические решения нелинейных уравнений с запаздыванием, используемых при математическом моделировании процессов переноса. Математическое моделирование и численные методы, 2024, № 3, с. 140–167.
Polyanin A. D. (Ishlinsky Institute for Problems in Mechanics), Sorokin V. G. (Ishlinsky Institute for Problems in Mechanics), Vyazmin A. V. (Moscow State University of Mechanical Engineering)
doi: 10.18698/2309-3684-2014-4-5373
In the article we explored nonlinear hyperbolic delay reaction-diffusion equations with varying transfer coefficients. A number of generalized separable solutions were obtained. Most of the equations considered contain arbitrary functions. Global nonlinear instability conditions of solutions of hyperbolic delay reaction-diffusion systems were determined. The generalized Stokes problem for a linear delay diffusion equation with periodic boundary conditions was solved.
Polyanin A., Sorokin V., Vyazmin A. Nonlinear delay reaction-diffusion equations of hyperbolic type: Exact solutions and global instability. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 53-73