Debopriya Mukherjee

Debopriya Mukherjee
Montanuniversität Leoben · Chair of Applied Mathematics

Doctor of Philosophy

About

10
Publications
741
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40
Citations

Publications

Publications (10)
Article
Full-text available
We investigate the existence of a weak martingale solution for a two-dimensional critical viscoelastic flow of the Oldroyd type driven by pure jump Lévy noise. Due to the viscoelastic nature, noise in the equation modeling stress tensor is considered in the Marcus canonical form. Owing to the lack of dissipation and taking into account of the struc...
Article
In this work, we consider sub-critical and critical models for viscoelastic flows driven by pure jump Lévy noise. Due to the elastic property, the noise in the equation for the stress tensor is considered in the Marcus canonical form. We investigate existence of a weak martingale solution for stochastic Oldroyd-B models, with full dissipation in wh...
Article
The stochastic Landau-Lifshitz-Gilbert equations (SLLGEs) describe the behaviour of the magnetisation under the influence of the randomly fluctuating effective field. In this work, we consider the SLLGEs in one space dimension in the presence of both the exchange energy and anisotropy energy and prove the existence of strong solution taking values...
Article
Full-text available
In this work we first present the existence, uniqueness and regularity of the strong solution of the tidal dynamics model perturbed by Levy noise. Monotonicity arguments have been exploited in the proofs. We then formulate a martingale problem of Stroock and Varadhan associated to an initial value control problem and establish existence of optimal...
Article
In this work we study stochastic Landau-Lifshitz-Gilbert equations (SLLGEs) in one dimension, with non-zero exchange energy only. Firstly, by introducing a suitable transformation, we convert the SLLGEs to a highly nonlinear time dependent partial differential equation with random coefficients, which is not fully parabolic. We then prove that there...
Preprint
The present paper deals with the interior solid-fluid interaction problem in harmonic regime where the unknowns are given by the stress tensor in the solid and the pressure in the fluid. Analysis of the shape derivative and shape Hessian of the solution is provided. Moments of the random solutions are approximated by those of the shape derivative a...
Preprint
In this work, we consider sub-critical and critical models for viscoelastic flows driven by pure jump Lévy noise. Due to the elastic property, the noise in the equation for the stress tensor is considered in the Marcus canonical form. We investigate existence of a weak martingale solution for stochastic Oldroyd-B models, with full dissipation in wh...
Article
Existence theory of optimal relaxed control problem for a class of stochastic hereditary evolution equations driven by Le'vy noise has been studied. We formulate the problem in the martingale sense of Stroock and Varadhan to establish existence of optimal controls. The construction of the solution is based on the classical Faedo-Galerkin approximat...
Article
Full-text available
In this work we study stochastic Oldroyd type models for viscoelastic fluids in $\mathbb{R}^d, d= 2, 3$. We show existence and uniqueness of strong local maximal solutions when the initial data are in $H^s$ for $s>d/2, d= 2, 3$. Probabilistic estimate of the random time interval for the existence of a local solution is expressed in terms of expecte...
Article
Full-text available
In this paper, we prove the stabilizability of abstract Parabolic Integro-Differential Equations (PIDE) in a Hilbert space with decay rate $e^{-\gamma t} $ for certain $\gamma > 0,$ by means of a finite dimensional controller in the feedback form. We determine a linear feedback law which is obtained by solving an algebraic Riccati equation. To prov...

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