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

  • 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.
    MSC: 35B40, 35B45, 35Q79, 80A
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