AIMS Mathematics, 2016, 1(1): 24-42. doi: 10.3934/Math.2016.1.24

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On the Caginalp phase-field system based on the Cattaneo law with nonlinear coupling

1 Universit´e des Sciences et techniques de Masuku, Franceville, Gabon
2 Universit´e de Poitiers, Laboratoire de Math´ematiques et Applications, UMR CNRS 7348 - SP2MI, Boulevard Marie et Pierre Curie - T´el´eport 2, F-86962 Chasseneuil Futuroscope Cedex, France

We focus in this paper on a Caginalp phase-field system based on the Cattaneo law with nonlinear coupling. We start our analysis by establishing existence, uniqueness and regularity based on Moser’s iterations. We finish with the study of the spatial behavior of the solutions in a semi-infinite cylinder, assuming the existence of such solutions.
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