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11:00am 
[11:00am] Sheetal Dharmatti : IISER Thiruvananthapuram.
 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 twodimensional bounded domain. The
CahnHilliardNavierStokes 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
CahnHilliardNavierStokes equations. We establish the firstorder
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.


12:00pm 
[12:00pm] Utpal Manna : IISER Thiruvananthapuram
 Description:
 Partial Differential Equations seminar
Speaker: Utpal Manna.
Affiliation: IISER Thiruvananthapuram.
Date and Time: Friday 12 July, 12:00 pm  1:00 pm.
Venue: Room 216, Department of Mathematics.
Title: Weak Solutions of a Stochastic Landau豊ifshitz萌ilbert Equation
Driven by Pure Jump Noise.
Abstract: In this work we study a stochastic threedimensional
LandauLifschitzGilbert equation perturbed by pure jump noise in the
Marcus canonical form. We show existence of weak martingale solutions
taking values in a twodimensional sphere $S^2$ and discuss certain
regularity results. The construction of the solution is based on the
classical FaedoGalerkin approximation, the compactness method and the
Jakubowski version of the Skorokhod Theorem for nonmetric spaces. This is
a joint work with Zdzislaw Brzezniak (University of York) and has been
published in Commun. Math. Phys. (2019),
https://doi.org/10.1007/s0022001903359x.


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