On a Caginalp phase-field system with a logarithmic nonlinearity

Applications of mathematics

Wehbe, Charbel¹ 

关键词: Caginalp phase-field system;    Dirichlet boundary conditions;    well-posedness;    long time behavior of solution;    global attractor;    exponential attractor;    Maxwell-Cattaneo law;    logarithmic potential;   

DOI  :  

学科分类：应用数学

来源: Akademie Ved Ceske Republiky

【 摘 要 】

We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.

【 授权许可】

Unknown