Fri, July 12, 2019
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July 2019
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11:00am [11:00am] Sheetal Dharmatti : IISER Thiruvananthapuram.
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.

12:00pm [12:00pm] Utpal Manna : IISER Thiruvananthapuram
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 three-dimensional Landau-Lifschitz-Gilbert equation perturbed by pure jump noise in the Marcus canonical form. We show existence of weak martingale solutions taking values in a two-dimensional sphere $S^2$ and discuss certain regularity results. The construction of the solution is based on the classical Faedo-Galerkin 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),