ON ANISOTROPIC CAGINALP PHASE-FIELD TYPE MODELS WITH SINGULAR NONLINEAR TERMS

Alain Miranville; Armel Judice Ntsokongo

doi:10.11948/2018.655

2018 Volume 8 Issue 3

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Alain Miranville, Armel Judice Ntsokongo. ON ANISOTROPIC CAGINALP PHASE-FIELD TYPE MODELS WITH SINGULAR NONLINEAR TERMS[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 655-674. doi: 10.11948/2018.655

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Alain Miranville, Armel Judice Ntsokongo. ON ANISOTROPIC CAGINALP PHASE-FIELD TYPE MODELS WITH SINGULAR NONLINEAR TERMS[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 655-674. doi: 10.11948/2018.655

ON ANISOTROPIC CAGINALP PHASE-FIELD TYPE MODELS WITH SINGULAR NONLINEAR TERMS

1 Xiamen University, School of Mathematical Sciences, Xiamen, Fujian, China;
2 Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348, Boulevard Marie et Pierre Curie, Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France;
3 Faculté des Sciences et Techniques, Université Marien Ngouabi, B. P. 69, Congo-Brazzaville

Abstract

Abstract

Our aim in this paper is to study the well-posedness and the existence of the global attractor of anisotropic Caginalp phase-field type models with singular nonlinear terms. The main difficulty is to prove, in one and two space dimensions, that the order parameter remains in the physically relevant range and this is achieved by deriving proper a priori estimates.
- Caginalp phase-field type models /
- anisotropy /
- singular nonlinear terms /
- well-posedness /
- global attractor
MSC: 35K55;35B41;35B45

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References

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