Exact solutions of linear and non-linear differential-difference heat and diffusion equations with finite relaxation timeстатья
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Дата последнего поиска статьи во внешних источниках: 12 февраля 2020 г.
Аннотация:We consider heat and diffusion equations with finite relaxation time which ensure a finite speed of propagation of disturbances. We use the Cattaneo–Vernotte model for the heat flux and obtain a number of exact solutions to the corresponding linear differential-difference heat equation. We also give exact solutions to two one-dimensional Stokes problem for a differential-difference mass/heat transfer equation (without a source and with a linear source) with a periodic boundary condition. We describe a number of exact solutions to non-linear differential-difference heat equations. In addition, we obtain some exact solutions to non-linear systems of two coupled reaction–diffusion equations with finite relaxation time and present several exact solutions of non-linear reaction–diffusion equations with time-varying delay. All equations in question contain arbitrary functions or free parameters. Their solutions can be used to solve certain problems and test numerical methods for non-linear partial differential-difference equations (delay partial differential equations).