Well-Posedness Analysis for a Linearization of a Fluid-Elasticity Interaction
Well-Posedness Analysis for a Linearization of a Fluid-Elasticity Interaction
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流体弹性相互作用线性化的适定性分析
DOI：
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发表时间：
2015
影响因子：
2
通讯作者：
J. Zolésio
中科院分区：
文献类型：
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作者：
L. Bociu;Daniel Toundykov;J. Zolésio
本文研究了自由边界非线性弹性-不可压缩流体相互作用在外力扰动下的完全线性化的适定性。最近，[L]对Navier-Stokes方程和非线性弹性动力学方程的耦合进行了完全线性化。博丘和J. - P. Zolesio，Evol.当量ag控制理论，2（2013），pp。55- 79]。将方程和自由边界一起线性化，结果与经典线性模型的通常耦合有很大不同。在公共界面上出现了新的附加项，其中一些涉及边界曲率和边界加速度。这些条款在最终的线性化系统中起着重要的作用，不能被忽视;他们的存在也引入了新的挑战，在适定性分析，从而建立相关的线性化系统的演化算子可以表示为一个最大的有界扰动…
We study the well-posedness of a total linearization, with respect to a perturbation of the external forcing, of a free-boundary nonlinear elasticity--incompressible fluid interaction. The total linearization for the coupling modeled by the Navier--Stokes equations and the nonlinear equations of elastodynamics was obtained recently in [L. Bociu and J.-P. Zolesio, Evol. Equ. Control Theory, 2 (2013), pp. 55--79]. The equations and the free boundary were linearized together, and the result turned out to be quite different from the usual coupling of classical linear models. New additional terms are present on the common interface, some of them involving boundary curvatures and boundary acceleration. These terms play an important role in the final linearized system and cannot be neglected; their presence also introduces new challenges in the well-posedness analysis, which proceeds to establish that the evolution operator associated to the linearized system can be represented as a bounded perturbation of a max...