6533b825fe1ef96bd1282032
RESEARCH PRODUCT
Energy dissipative solutions to the Kobayashi-Warren-Carter system
Salvador MollKen ShirakawaHiroshi Watanabesubject
Applied Mathematics010102 general mathematicsGeneral Physics and AstronomyStatistical and Nonlinear Physics010103 numerical & computational mathematicsDissipation01 natural sciencesMathematics - Analysis of PDEs35K87 35R06 35K67Regularization (physics)FOS: MathematicsDissipative systemApplied mathematics0101 mathematicsMathematical PhysicsAnalysis of PDEs (math.AP)Energy functionalMathematicsdescription
In this paper we study a variational system of two parabolic PDEs, called the Kobayashi-Warren-Carter system, which models the grain boundary motion in a polycrystal. The focus of the study is the existence of solutions to this system which dissipate the associated energy functional. We obtain existence of this type of solutions via a suitable approximation of the energy functional with Laplacians and an extra regularization of the weighted total variation term of the energy. As a byproduct of this result, we also prove some $\Gamma$-convergence results concerning weighted total variations and the corresponding time-dependent cases. Finally, the regularity obtained for the solutions together with the energy dissipation property, permits us to completely characterize the $\omega$-limit set of the solutions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-02-13 |