Functional separable solutions of nonlinear reaction–diffusion equations with variable coefficients

Andrei D. Polyanin

Applied Mathematics and Computation, 2019, vol. 347, issue C, 282-292

Abstract: The paper presents a number of new functional separable solutions to nonlinear reaction–diffusion equations of the formc(x)ut=[a(x)ux]x+b(x)ux+p(x)f(u),where f(u) is an arbitrary function. It is shown that any three of the four variable coefficients a(x), b(x), c(x), p(x) of such equations can be chosen arbitrarily, and the remaining coefficient can be expressed through the others. Examples of specific equations and their exact solutions are given. The results obtained are generalized to more complex multidimensional nonlinear reaction–diffusion equations with variable coefficients. Also some functional separable solutions to nonlinear reaction–diffusion equations with delayut=uxx+a(x)f(u,w),w=u(x,t−τ),where τ > 0 is the delay time and f(u, w) is an arbitrary function of two arguments, are obtained.

Keywords: Nonlinear reaction–diffusion equations; Reaction–diffusion equations with delay; Equations with variable coefficients; Exact solutions; Functional separable solutions (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630031830972X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:347:y:2019:i:c:p:282-292

DOI: 10.1016/j.amc.2018.10.092

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().