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 Navieräº¡tokes equation

governing the fluid velocity field coupled with a convective Cahnè“¬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.

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 Navieräº¡tokes equation

governing the fluid velocity field coupled with a convective Cahnè“¬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.

Description

Room No. 216 Department of Mathematics

Date

Fri, July 12, 2019

Start Time

11:00am IST

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Tue, July 9, 2019 2:41pm IST