WEAK SOLUTION TO THE INCOMPRESSIBLE VISCOUS FLUID AND A THERMOELASTIC PLATE INTERACTION PROBLEM IN 3D

• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 19-38
• 页数: 20页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2021.01.002

摘要

In this paper we deal with a nonlinear interaction problem between an incom-pressible viscous fluid and a nonlinear thermoelastic plate.The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models.We prove the existence of a weak solution for this problem by con-structing a hybrid approximation scheme that,via operator splitting,decouples the system into two sub-problems,one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure.To prove the convergence of the approximate quasilin-ear elastic force,we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.