Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay

Andrei D. Polyanin () and Vsevolod G. Sorokin ()
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Andrei D. Polyanin: Ishlinsky Institute for Problems in Mechanics RAS, 101 Vernadsky Avenue, bldg 1, 119526 Moscow, Russia
Vsevolod G. Sorokin: Ishlinsky Institute for Problems in Mechanics RAS, 101 Vernadsky Avenue, bldg 1, 119526 Moscow, Russia

Mathematics, 2023, vol. 11, issue 14, 1-19

Abstract: This study is devoted to reaction–diffusion equations with spatially anisotropic time delay. Reaction–diffusion PDEs with either constant or variable transfer coefficients are considered. Nonlinear equations of a fairly general form containing one, two, or more arbitrary functions and free parameters are analyzed. For the first time, reductions and exact solutions for such complex delay PDEs are constructed. Additive, multiplicative, generalized, and functional separable solutions and some other exact solutions are presented. In addition to reaction–diffusion equations, wave-type PDEs with spatially anisotropic time delay are considered. Overall, more than twenty new exact solutions to reaction–diffusion and wave-type equations with anisotropic time delay are found. The described nonlinear delay PDEs and their solutions can be used to formulate test problems applicable to the verification of approximate analytical and numerical methods for solving complex PDEs with variable delay.

Keywords: nonlinear reaction–diffusion equations; PDEs with variable delay; spatially anisotropic time delay; wave-type equations; partial functional-differential equations; exact solutions; reductions; additive and multiplicative separable solutions; generalized and functional separable solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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