| Abstract: |
| In this talk, we consider a system of pseudo-parabolic PDEs, which is derived as a dissipation system (gradient flow) of a non-smooth functional. In this context, the governing functional is often called Kobayashi--Warren--Carter type energy (KWC type energy), and it is known as a free-energy of planar grain boundary motion, proposed by [Kobayashi et al., Physica D, 140, 141--150 (2000)]. The mathematical characteristics of our system is in the point that the pseudo-parabolicity yields stronger regularity than that in parabolic gradient flow, while the governing free-energy is non-smooth. Therefore, it would be expected that our energy dissipation system would be a distinct mathematical model of grain boundary motion, and furthermore, it would provide a mathematical method of minimization process governed by non-smooth energy. The objective of this study is to obtain some theoretical estimate for this expectation. As a part of the estimate, the mathematical issues concerned with the existence, uniqueness, continuous dependence, large-time behavior, and so on, will be discussed in the Main Theorems of this talk. |
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