论文标题
关于抛物线类型的非线性问题，具有涉及通量的隐式本构方程
On nonlinear problems of parabolic type with implicit constitutive equations involving flux
论文作者
论文摘要
我们研究了抛物线类型的非线性偏微分方程的系统，其中椭圆运算符被作用于通量函数的一阶差异操作员所取代，该操作员通过附加隐式方程与未知的空间梯度有关。这种环境在应用方面足够广泛，大大扩大了非线性抛物线问题的范式。制定有关隐式方程式形式的四个条件，我们首先表明这些条件描述了最大单调$ p $ - 驾驶图。然后，我们建立了（弱）解决方案及其独特性的全球时间和大数据。为了实现这一目标，我们采用并显着概括了单调映射的minty方法。一个包含多种新工具的统一理论是以数字拖延的方式开发的。
We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone $p$-coercive graph. We then establish the global-in-time and large-data existence of (weak) solution and its uniqueness. Towards this goal, we adopt and significantly generalize the Minty method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable numerically.
