论文标题
二阶的抽象非线性进化包含在Visco-elasto塑性中的应用
Abstract nonlinear evolution inclusions of second order with applications in visco-elasto-plasticity
论文作者
论文摘要
通过半无限时间离散化方法确定了一类非线性进化包含的一类非线性进化包含的cauchy问题的强大解决方案。在$ u $和$ u'$上作用的运营商的主要部分是多价划分的操作员，并隐式地将其离散化。允许并及时明确地显式地显式地将非变化的和非偶然的扰动代理非线性和$ u'$。使用凸分析中的方法建立了变分近似方案的收敛性。另外，证明该解决方案满足了能量散落的平等。提供了抽象理论在各种示例中的应用，例如，提供了粘弹性塑性性的模型。
Existence of strong solutions of an abstract Cauchy problem for a class of doubly nonlinear evolution inclusion of second order is established via a semi-implicit time discretization method. The principal parts of the operators acting on $u$ and $u'$ are multi-valued subdifferential operators and are discretized implicitly. A non-variational and non-monotone perturbation acting nonlineary on $u$ and $u'$ is allowed and discretized explicitly in time. The convergence of a variational approximation scheme is established using methods from convex analysis. In addition, it is proven that the solution satisfies an energy-dissipation equality. Applications of the abstract theory to various examples, e.g., a model in visco-elastic-plasticity, are provided.
