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Research Article Open access CC BY 4.0

Attractors and Numerical Simulations for a Two-Temperature Phase Transition System

Mohamed Ali Ipopa, Brice Landry Doumbe Bangola, Armel Andami Ovono

Journal of Advances in Mathematics and Computer Science · pp. 99–116 · Published 26 Dec 2022

10.9734/jamcs/2022/v37i121732

Abstract

In this paper, we study a generalisation of the Caginalp phase field system obtained by considering the Fourier law as the heat conduction law and involving two temperatures. In the first section, we are interested in the existence and uniqueness of solutions. In section 2, we address the question of the asymptotic behaviour of the solutions, in particular with the demonstration of the existence of a global attractor. For this, we needed to show that the system is dissipative  and to  know the regularity  of the  solutions. Finally,  in  the last  section, we turn to the numerical solution of our problem.

Caginalp phase-field system two temperatures global attractor semigroup decomposition method

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Cited by 4

Asymptotic behaviour of a phase field system derived from a generalization of Maxwell–Cattaneo’s law with a singular potential

Brice Landry Doumbé Bangola, Mohamed Ali Ipopa, Armel Andami Ovono · Journal of Physics A: Mathematical and Theoretical · 2024

Asymptotic Behavior and Numerical Simulations of a Conservative Phase-Field Model with Two Temperatures

Brice Landry Doumbé Bangola, Mohamed Ali Ipopa, Armel Andami Ovono · Journal of Nonlinear Mathematical Physics · 2024

On the Spatial Behaviour for Solutions to a Phase Transition Model Involving Two Temperatures

Mohamed Ali IPOPA, Brice Landry Doumbé Bangola, Jean De Dieu MANGOUBI · Contemporary Mathematics · 2025

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