Work

Stability properties of solutions to convection-reaction equations with nonlinear diffusion

Year: 2025

Type: article

Abstract: In this paper we study a convection-reaction-diffusion equation of the form $ u_t = \varepsilon(h(u)u_x)_x-f(u)_x+f'(u), \; \; t > 0, $ with a nonlinear diffusion in a bounded interval of the real line. In particular, we first focus our attention on the existence of stationary solutions with at most one zero inside the interval, studying their behavior with respect to the viscosity coefficient $ \varepsilon > 0 $ and their stability/instability properties. Then, we investigate the large time behavior of the solutions for finite times and the asymptotic regime. We also show numerically that, for a particular class of initial data, the so-called metastable behavior occurs, meaning that the time-dependent solution persists for an exponentially long (with respect to $ \varepsilon $) time in a transition non-stable phase, before converging to a stable configuration.

Source: Mathematics in Engineering

Authors: Alessandro Alla, Alessandra De Luca, Raffaele Folino, Marta Strani, Departamento de Matemáticas y Mecánica, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Circuito Escolar s/n, C.P. 04510 Cd. de México, México

Institutions: Sapienza University of Rome, University of Turin, Universidad Nacional Autónoma de México, Ca' Foscari University of Venice

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond