webcal

Description

Partial Differential Equations seminar.

Speaker: Sheetal Dharmatti.

Affiliation: IISER Thiruvananthapuram.

Date and Time: Friday 12 July, 11:00 am - 12:00 pm.

Venue: Room 216, Department of Mathematics.

Title: Data assimilation type Optimal control problem for Cahn Hilliard
Navier Stokes' system.

Abstract: This work is concerned about some optimal control problems
associated to the evolution of two isothermal, incompressible, immiscible
fluids in a two-dimensional bounded domain. The
Cahn-Hilliard-Navier-Stokes model consists of a Navier亡tokes equation
governing the fluid velocity field coupled with a convective Cahn蓬illiard
equation for the relative concentration of one of the fluids. A
distributed optimal control problem is formulated as the minimization of a
cost functional subject to the controlled nonlocal
Cahn-Hilliard-Navier-Stokes equations. We establish the first-order
necessary conditions of optimality by proving the Pontryagin maximum
principle for optimal control of such system via the seminal Ekeland
variational principle. The optimal control is characterized using the
adjoint variable. We also study another control problem which is similar
to that of data assimilation problems in meteorology of obtaining unknown
initial data using optimal control techniques when the underlying system
is same as above.

Sheetal Dharmatti : IISER Thiruvananthapuram.