Work

Generalized Reaction-Diffusion Equation With Density Dependent Diffusion

Year: 2026

Type: article

Abstract: Existence theorem for the traveling wave solutions of the “generalized” nonlinear reaction-diffusion equation $u_{t}=(u^{m})_{xx}+f(u),$ is established for any $m>1.$ This form generalizes the classical linear form with $m=1.$ A critical value of the minimum wave speed $c^{*}$ is obtained as $c^{*}=2m\sqrt{f^{\prime }(0)}$ , which extends the results obtained by Fisher, Kolmogorov, and others.

Source: Journal of Nonlinear Mathematical Physics

DOI: 10.1007/s44198-026-00435-4

Authors: Lazhar Bougoffa, Ammar Khanfer

Institutions: Imam Mohammad ibn Saud Islamic University, Prince Sultan University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,490

Funder: Deanship of Scientific Research, Imam Mohammed Ibn Saud Islamic University