论文标题
部分微分方程某些系统的功能耗散性
The functional dissipativity of certain systems of partial differential equations
论文作者
论文摘要
在本文中，我们考虑了dirichlet问题的功能耗散性，用于$ \ partial_ {h}的部分差分操作员的系统（{\ Mathop {\ Mathop {\ mathscr a} \ nolimits} \ nolimits}^{hk} {hk} { a} \ nolimits}^{hk} $为$ m \ times m $矩阵，具有复杂的$ l^{1} _ {\ text {loc}} $ entries）。在操作员的特殊情况下，$ \ partial_ {h}（{\ Mathop {\ MathScr a} \ nolimits} \ nolimits}^{h}^{h}（x）\ partial_ {h}）$（其中$ {\ m athop {\ sathscr {\ mathscr a} \ nolimits a} \ nolimits}必要和充分的条件。我们还给出了三种不同的功能椭圆度概念，并研究了它们之间的关系以及有关操作员的功能耗散性。
In the present paper we consider the functional dissipativity of the Dirichlet problem for systems of partial differential operators of the form $\partial_{h} ({\mathop{\mathscr A}\nolimits}^{hk}(x)\partial_{k})$ (${\mathop{\mathscr A}\nolimits}^{hk}$ being $m\times m$ matrices with complex valued $L^{1}_{\text{loc}}$ entries). In the particular case of the operator $\partial_{h} ({\mathop{\mathscr A}\nolimits}^{h}(x)\partial_{h})$ (where ${\mathop{\mathscr A}\nolimits}^{h}$ are $m\times m$ matrices) we obtain algebraic necessary and sufficient conditions. We give also three different notions of functional ellipticity and investigate the relations between them and the functional dissipativity for the operators in question.
