ON THE CAGINALP PHASE-FIELD SYSTEM BASED ON TYPE Ⅲ WITH TWO TEMPERATURES AND NONLINEAR COUPLING

Armel Andami Ovono; Brice Doumbe Bangola; Mohamed Ali Ipopa

doi:10.11948/2019.345

2019 Volume 9 Issue 1

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Armel Andami Ovono, Brice Doumbe Bangola, Mohamed Ali Ipopa. ON THE CAGINALP PHASE-FIELD SYSTEM BASED ON TYPE Ⅲ WITH TWO TEMPERATURES AND NONLINEAR COUPLING[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 345-362. doi: 10.11948/2019.345

Citation:

Armel Andami Ovono, Brice Doumbe Bangola, Mohamed Ali Ipopa. ON THE CAGINALP PHASE-FIELD SYSTEM BASED ON TYPE Ⅲ WITH TWO TEMPERATURES AND NONLINEAR COUPLING[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 345-362. doi: 10.11948/2019.345

ON THE CAGINALP PHASE-FIELD SYSTEM BASED ON TYPE Ⅲ WITH TWO TEMPERATURES AND NONLINEAR COUPLING

1.
Laboratoire de Mathématiques et de Physique Appliquée, Masuku University, BP 943 Franceville, Gabon
2.
Département de Mathématiques, Masuku University, BP 943 Franceville, Gabon
3.
Laboratoire de Mathématiques et de Physique Appliquée, Masuku University, BP 943 Franceville, Gabon

Author Bio: Email address: lecolombien2000@yahoo.fr(B. Doumbe Bangola); Email address: ipopa.mohamed@hotmail.fr(M. A. Ipopa)
Corresponding author: Email address: andami@math.univ-poitiers.fr(A. Andami Ovono)

Abstract

Abstract

This paper is devoted to the study of a generalization of the Caginalp phase-field system based on the theory of type Ⅲ thermomechanics with two temperatures for the heat conduction with a nonlinear coupling term. We start our analysis by establishing existence of the solutions. Then, we discuss dissipativity and uniqueness of the solutions. We finish our analysis by studying the spatial behavior of the solutions in a semi-infinite cylinder, assuming the existence of such solutions.
- Caginalp system /
- nonlinear coupling /
- type Ⅲ /
- spatial behaviour
MSC: 35B40, 35B45, 35Q79, 80A

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References

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