Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay

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 parameter...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics (Basel) 2023-07, Vol.11 (14), p.3111
Main Authors: Polyanin, Andrei D., Sorokin, Vsevolod G.
Format: Article
Language:English
Subjects:
Anisotropy
Control theory
Exact solutions
Nonlinear equations
nonlinear reaction–diffusion equations
Numerical analysis
Numerical methods
Ordinary differential equations
Partial differential equations
partial functional-differential equations
PDEs with variable delay
Reaction-diffusion equations
spatially anisotropic time delay
Time lag
wave-type equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11143111