论文标题
多价非单子酮动态边界条件
Multivalued nonmonotone dynamic boundary condition
论文作者
论文摘要
在本文中，我们介绍了一种新的半因不平等现象，称为动态边界半传子不平等现象，反映了管理操作员在边界上也有效的事实。在我们的上下文中，它涉及拉普拉斯操作员的wentzell（动态）边界条件，该条件受到以克拉克亚差异为表示的多晕非单子酮操作员的扰动。我们将证明可以重新制定问题，以便可以应用标准技术。我们将使用良好的边界半传向不平等的理论来证明，在生长和一般的符号条件下，动态边界半偏向不平等的解决方案肯定了薄弱的解决方案。此外，在用局部界面的集成表达功能的情况下，在不连续点处的“填充间隙”过程用于表征产品空间上的子不同。最后，我们证明，在生长条件并最终较小的条件下，Faedo-Galerkin近似序列会收敛到所需溶液。
In this paper, we introduce a new class of hemivariational inequalities, called dynamic boundary hemivariational inequalities reflecting the fact that the governing operator is also active on the boundary. In our context, it concerns the Laplace operator with Wentzell (dynamic) boundary conditions perturbed by a multivalued nonmonotone operator expressed in terms of Clarke subdifferentials. We will show that one can reformulate the problem so that standard techniques can be applied. We will use the well-established theory of boundary hemivariational inequalities to prove that under growth and general sign conditions, the dynamic boundary hemivariational inequality admits a weak solution. Moreover, in the situation where the functionals are expressed in terms of locally bounded integrands, a "filling in the gaps" procedure at the discontinuity points is used to characterize the subdifferential on the product space. Finally, we prove that, under a growth condition and eventually smallness conditions, Faedo-Galerkin approximation sequence converges to a desired solution.
