论文标题
耦合准线性抛物线方程和线性双曲系统的模型的存在结果
Existence Result For a Model Coupling a Quasi-Linear Parabolic Equation and a Linear Hyperbolic System
论文作者
论文摘要
我们证明了与线性线性系统和准线性stokes方程相连的问题的全球存在解决方案。这个全局耦合问题的解决方案被视为某些非线性操作员$ t $的固定点。我们使用正规化过程构建了辅助近似紧凑型运算符的序列$（t^ε）_ε$。然后，我们使用Banach和Schaeffer固定点定理的组合建立了对每个操作员$ t^ε$的固定点的存在。最后，我们证明这些固定点会收敛到$ t $的固定点
We prove globally-in-time existence of solution for a problem coupling the linear Lamé system and the quasi-linear Stokes equation. A solution of this global coupled problem is viewed as the fixed point of some non-linear operator $T$. We construct, using a regularization procedure, a sequence $(T^ε)_ε$ of auxiliary approximating compact operators. Then we establish, using a combination of Banach and Schaeffer fixed point theorems, the existence of fixed points to every operator $T^ε$. Finally we prove that these fixed points converge to the fixed point of $T$
