Parameter identification problem for the equation of motion of membrane with strong viscosity

Abstract

The parameter identification problem of constant parameters in the equation of membrane with strong viscosity is studied. The problem is formulated by a minimization of quadratic cost functionals by distributive measurements. The existence of optimal parameters and necessary optimality conditions for the parameters are proved.

Weak and Strong Solutions for a Strongly Damped Quasilinear Membrane Equation

“…Besides, the well-posedness of less regular solutions is proved in [1], called weak solutions in the framework of the variational method in Dautray and Lions [3]. Based on these results, we have treated the associated optimal control and identification problems in [6] and [7], respectively. Furthermore, in [8] we have extended the results in [1] to more general quasilinear nonautonomous wave equation with strong damping term.…”

Parameter identification problems for an extensible beam equation

“…However, we can find a few articles which extend the identification problems to practical nonlinear PDEs. Quite recently, Hwang and Nakagiri [9] studied the identification problems for the equation of vibration of an elastic membrane represented by a quasilinear parabolic PDE.…”