517.929+517.95 Analytical solutions of nonlinear transport equations with delay

Sorokin V. G. (Ishlinsky Institute for Problems in Mechanics)

NONLINEAR TRANSPORT EQUATIONS WITH DELAY, DELAY PARTIAL DIFFERENTIAL EQUATIONS, ANALYTICAL SOLUTIONS, GENERALIZED AND FUNCTIONAL SEPARABLE SOLUTIONS, SELF-SIMILAR SOLUTIONS


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.


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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.


Работа выполнена по теме государственного задания (№ госрегистрации 124012500440-9).


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