L1-Theory for Hele-Shaw Flow with Linear Drift
L1-Theory for Hele-Shaw Flow with Linear Drift
复制标题
线性漂移 Hele-Shaw 流的 L1 理论
DOI：
--
复制
发表时间：
2021
影响因子：
3.5
通讯作者：
N. Igbida
中科院分区：
文献类型：
--
作者：
N. Igbida
本文的主要目的是证明具有线性漂移的Hele-Shaw流的弱解（在分布意义下）的L^1 $-比较原理和压缩原理。流动被认为是一个一般的反应项，包括Lipschitz连续的情况下，并受到混合均匀的边界条件：狄利克雷和诺依曼。我们的方法结合了DiPerna-Lions重整化类型和Kruzhkov设备的加倍和去加倍变量。$L^1$-压缩原理允许以后在$L^1中的非线性半群理论的一般框架中处理该问题，从而利用这个强理论来研究弱解的存在性、唯一性、比较、$L^1$-稳定性以及许多进一步的问题。
The main goal of this paper is to prove $L^1$-comparison and contraction principles for weak solutions (in the sense of distributions) of Hele-Shaw flow with a linear Drift. The flow is considered with a general reaction term including the Lipschitz continuous case, and subject to mixed homogeneous boundary conditions : Dirichlet and Neumann. Our approach combines DiPerna-Lions renormalization type with Kruzhkov device of doubling and de-doubling variables. The $L^1$-contraction principle allows afterwards to handle the problem in a general framework of nonlinear semigroup theory in $L^1,$ taking thus advantage of this strong theory to study existence, uniqueness, comparison of weak solutions, $L^1$-stability as well as many further questions.