论文标题
具有完全不可逆性和节能的演化方程
Evolution equations with complete irreversibility and energy conservation
论文作者
论文摘要
本文涉及符合三种固有特性的进化变异不平等的初始价值问题：完全不可逆性，能量的单方面平衡和能量保护定律，通常在耗散系统（例如标准渐变流量）中实现。主要结果包括良好的配方，强大的溶液的定性特性（即比较原理和上述三个特性）以及强溶液的长期动力学（更确切地说，更确切地说是融合到平衡）。适当的性能将基于最小化的运动方案而没有抛物线抛物面化，这也将在证明强溶液的定性和渐近性特性方面起着至关重要的作用。此外，所考虑的变异不平等将被视为某些（广义）梯度流的单一极限。
This paper is concerned with the initial-boundary value problem for an evolutionary variational inequality complying with three intrinsic properties: complete irreversibility, unilateral equilibrium of an energy and an energy conservation law, which cannot generally be realized in dissipative systems such as standard gradient flows. Main results consist of well-posedness in a strong formulation, qualitative properties of strong solutions (i.e., comparison principle and the three properties mentioned above) and long-time dynamics of strong solutions (more precisely, convergence to an equilibrium). The well-posedness will be proved based on a minimizing movement scheme without parabolic regularization, which will also play a crucial role for proving qualitative and asymptotic properties of strong solutions. Moreover, the variational inequality under consideration will be characterized as a singular limit of some (generalized) gradient flows.
