多值非单调动力边界条件
Multivalued nonmonotone dynamic boundary condition
摘要：
本文引入了一类新的半变分不等式，称为动态边界半变分不等式，它反映了控制算子在边界上也是活动的。在我们的上下文中，它涉及的拉普拉斯算子与Wentzell（动态）边界条件扰动的多值非单调运营商表示的克拉克次微分。我们将表明，一个可以重新制定的问题，使标准技术可以应用。利用边界半变分不等式理论证明了在增长和一般符号条件下，动态边界半变分不等式存在弱解.此外，在泛函用局部有界被积函数表示的情况下，在不连续点处采用“填补空隙”的方法刻画了积空间上的次微分.最后，我们证明了，在增长条件和最终小的条件下，Faedo-Galerkin逼近序列收敛到一个期望的解决方案。
英文摘要：
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.
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