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

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

doi:10.9734/jamcs/2022/v37i121732

JAMCS

2022

DOI: 10.9734/jamcs/2022/v37i121732

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

Mohamed Ali Ipopa

Brice Landry Doumbe Bangola²,

Armel Andami Ovono³

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 t… Show more

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2024

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Cited by 2 publications

References 30 publications

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

Doumbe Bangola,

Ipopa,

Andami Ovono

2024

J Nonlinear Math Phys

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One of the types of problem that has attracted the attention of mathematicians in recent years is the phase field system. The field of application includes materials science, where phenomena such as phase separation in alloys, crystal formation and thermal welding are legion. Among these phase transition systems, the family of conservative systems is very popular with industry. Indeed, minimising losses in production systems is a major issue for their profitability. In this paper, we study the well-posedness of the formulation and the asymptotic behaviour of the solutions, by proving the existence of a finite-dimensional global attractor for a conservative variant of the two-temperature phase field system with homogeneous Neumann boundary conditions. The inclusion of two temperatures in the definition of the enthalpy of the system is a necessity in the case of a non-simple material. In a simple material, once the phase-change temperature has been reached, the temperature of the system remains constant until the material has completely changed state. This is not true in the case of a non-simple material, where an increase in the temperature of the system is observed even after the phase-change temperature has been reached. To conclude the work, we present a method for numerically approximating the solution and carry out some numerical tests.

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

Doumbe Bangola,

Ipopa,

Andami Ovono

2024

J Nonlinear Math Phys

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

Landry Doumbé Bangola,

Ali Ipopa,

Andami Ovono

2024

J. Phys. A: Math. Theor.

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In this paper, we study the asymptotic behaviour of a Caginalp-type phase ﬁeld system derived from a heat conduction law which is a generalization of the Maxwell-Cattano law and whose potential is singular. This type of law has the advantage of correcting the paradox of heat conduction that appears when the Fourier law is considered. The potential considered is typically logarithmic. Using such a potential makes the model much more relevant from a physical point of view. However, from a theoretical point of view, it is essential to obtain the property of strict separation of the order parameter in order to make sense of the equations. We ﬁrst prove the existence and uniqueness of the solution thanks to the separation property. We also address the question of the dissipativity of the system. Finally, we obtain the existence of the global attractor.

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

Cited by 2 publications

References 30 publications

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

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

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

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