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

In this paper we deal with a nonlinear interaction problem between an incompressible 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 constructing 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 quasilinear elastic force,we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.