On a Cahn-Hilliard/Allen-Cahn system coupled with a type III heat equation and singular potentials. (English) Zbl 1444.35026
The authors consider the Cahn-Hilliard/Allen-Cahn system coupled with the type III heat conduction. In a first step, they obtain several “a priori estimates” that allow them to show the existence of weak solutions in the case of a singular nonlinear term (logarithmic is also included). It is worth saying that thermodynamically relevant functions satisfy the required conditions for the nonlinear term. The approximation to the problem is done by means of a regular approximation to the singular nonlinear term. Uniqueness of solutions is also obtained and the existence of a semigroup is guaranteed. Higher-order regularity results ends the paper. This is a nice paper.
Reviewer: Ramón Quintanilla de Latorre (Barcelona)
MSC:
| 35G61 | Initial-boundary value problems for systems of nonlinear higher-order PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35B45 | A priori estimates in context of PDEs |
Keywords:
Cahn-Hilliard/Allen-Cahn equations; type III heat conduction; logarithmic nonlinear terms; well-posedness; dissipativity; parabolic-hyperbolic systemReferences:
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