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Title The phase-field transition system endowed with a general regular potential and nonlinear dynamic boundary conditions of non-homogeneous type and non-constant thermal conductivity

Name Costica N Morosanu
Country Romania
Email costica.morosanu@uaic.ro
Submit Time 2014-02-17 12:43:14
Special Session 2: Nonlinear evolution PDEs and interfaces in applied sciences
{{\bf Abstract.} The work is devoted to the study of a Caginalp phase-field transition system, endowed with a general regular potential and a general class of nonlinear and non-homogeneous dynamic boundary conditions (in both unknown functions), as well as non-constant thermal conductivity. The existence, uniqueness and regularity of solutions is established. This extends previous works, including the already studied boundary conditions, which makes the preset mathematical model capable to reveal the complexity of the real physical phenomena, including the phase change.} \medskip \item {~~}{{\bf Key words.} Nonlinear initial-boundary value problems, nonlinear parabolic systems, dynamic boundary conditions, Leray-Schauder principle, Nemytskij's operator, thermodynamics, phase-field models.} \medskip \item {~~}{{\bf Subject classification.} 35B65, 35K61, 35Q56, 47H30, 74A15, 80A22.}