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On the Caginalp phase-field system based on type III with two temperatures and nonlinear coupling.
Keywords:Caginalp system, nonlinear coupling, type III, spatial behaviour.
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.