arXiv subjects

Mythily Ramaswamy

Publications and source records attributed to Mythily Ramaswamy.

6 recordsLinked to original sources

arXiv2023

Feedback stabilization of parabolic coupled system and its numerical study

In the first part of this article, we study feedback stabilization of a parabolic coupled system by using localized interior controls. The system is feedback stabilizable with exponential decay $-ω<0$ for any $ω>0$. A stabilizing control is found in feedback form by solving a suitable algebraic Riccati equation. In the second part, a conforming finite element method is employed to approximate the continuous system by a finite dimensional discrete system. The approximated system is also feedback stabilizable (uniformly) with exponential decay $-ω+ε$, for any $ε>0$ and the feedback control is obtained by solving a discrete algebraic Riccati equation. The error estimate of stabilized solutions as well as stabilizing feedback controls are obtained. We validate the theoretical results by numerical implementations.

math.AP↗

arXiv2020

Remark on the global null controllability for a viscous Burgers-particle system with particle supported control

This paper is devoted to study the controllability of a one-dimensional fluid-particle interaction model where the fluid follows the viscous Burgers equation and the point mass obeys Newton's second law. We prove the null controllability for the velocity of the fluid and the particle and an approximate controllability for the position of the particle with a control variable acting only on the particle. One of the novelties of our work is the fact that we achieve this controllability result in a uniform time for all initial data and without any smallness assumptions on the initial data.

math.AP↗

arXiv2019

Self-propelled motion of a rigid body inside a density dependent incompressible fluid

This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous Navier-Stokes system with a nonnegative density. The motion of the rigid body is described by the balance of linear and angular momentum. We consider the case where slip is allowed at the fluid-solid interface through Navier condition and prove the global existence of a weak solution.

math.AP↗

arXiv2016

Observers for compressible Navier-Stokes equation

We consider a multi-dimensional model of a compressible fluid in a bounded domain. We want to estimate the density and velocity of the fluid, based on the observations for only velocity. We build an observer exploiting the symmetries of the fluid dynamics laws. Our main result is that for the linearised system with full observations of the velocity field, we can find an observer which converges to the true state of the system at any desired convergence rate for finitely many but arbitrarily large number of Fourier modes. Our one-dimensional numerical results corroborate the results for the linearised, fully observed system, and also show similar convergence for the full nonlinear system and also for the case when the velocity field is observed only over a subdomain.

math.OC↗

arXiv2015

Radial Symmetry on 3D Shells in the Landau-de Gennes Theory

We study the stability of the radial-hedgehog solution on a three-dimensional (3D) spherical shell with radial boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. We show that the radial-hedgehog solution has no zeroes for a sufficiently narrow shell, for all temperatures below the nematic supercooling temperature. We prove that the radial-hedgehog solution is the unique global Landau-de Gennes energy minimizer for a sufficiently narrow 3D spherical shell, for all temperatures below the nematic supercooling temperature. We provide explicit geometry-dependent criteria for the global minimality of the radial-hedgehog solution in this temperature regime. In the low temperature limit, we prove the global minimality of the radial-hedgehog solution on a 3D spherical shell, for all values of the inner and outer radii.

math.AP↗

arXiv2008

Unbounded Viscosity Solutions of Hybrid Control Systems

We study a hybrid control system in which both discrete and continuous controls are involved. The discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set $A$ or a controlled jump set $C$ where controller can choose to jump or not. At each jump, trajectory can move to a different Euclidean space. We allow the cost functionals to be unbounded with certain growth and hence the corresponding value function can be unbounded. We characterize the value function as the unique viscosity solution of the associated quasivariational inequality in a suitable function class. We also consider the evolutionary, finite horizon hybrid control problem with similar model and prove that the value function is the unique viscosity solution in the continuous function class while allowing cost functionals as well as the dynamics to be unbounded.

math.AP↗