arXiv subjects

Mrinmay Biswas

Publications and source records attributed to Mrinmay Biswas.

6 recordsLinked to original sources

arXiv2026

Approximate Controllability of the generalized Burgers-Huxley equation in one dimension

The generalized Burgers-Huxley (GBH) equation is a prototype model that describes the interplay among reaction, convection, and diffusion. In this article, we explore the controllability of this model by means of an interior control supported in an arbitrary non-empty open subset of the domain. We establish that the GBH equation is not globally approximately controllable in a given time. However, it is possible to steer the system from any steady state to an arbitrarily small neighborhood of another steady state in some suitable time by means of a localized interior control, provided that both steady states lie in the same connected component of the set of steady states.

math.OC↗

arXiv2026

Strong convergence of finite element approximations for a fourth-order stochastic pseudo-parabolic equation with additive noise

In this article, we analyze semi-discrete finite element approximation and full discretization of a fourth-order stochastic pseudo-parabolic equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite element method for spatial discretization and the semi-implicit method for temporal discretization, and obtain strong convergence rates with respect to both the spatial and temporal mesh sizes. Numerical experiments are presented to support the theoretical convergence rates.

math.NA↗

arXiv2026

Finite Element Approximations of Stochastic Linear Schrödinger equation driven by additive Wiener noise

In this article, we have analyzed semi-discrete finite element approximations of the Stochastic linear Schrödinger equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite element method for spatial discretization and derive an error estimate with respect to the discretization parameter of the finite element approximation. Numerical experiments have also been performed to support theoretical bounds.

math.NA↗

arXiv2025

Full Discretization of Stochastic Semilinear Schrödinger equation driven by multiplicative Wiener noise

In this article, we have analyzed the full discretization of the Stochastic semilinear Schrödinger equation in a bounded convex polygonal domain driven by multiplicative Wiener noise. We use the finite element method for spatial discretization and the stochastic trigonometric method for time discretization and derive a strong convergence rate with respect to both parameters (temporal and spatial). Numerical experiments have also been performed to support theoretical bounds.

math.NA↗

arXiv2022

Global martingale solutions to a segregation cross-diffusion system with stochastic forcing

The existence of a global martingale solution to a cross-diffusion system with multiplicative Wiener noise in a bounded domain with no-flux boundary conditions is shown. The model describes the dynamics of population densities of different species due to segregation cross-diffusion effects. The diffusion matrix is generally neither symmetric nor positive semidefinite. This difficulty is overcome by exploiting the Rao entropy structure. The existence proof uses a stochastic Galerkin method, uniform estimates from the Rao entropy inequality, and the Skorokhod--Jakubowski theorem. Furthermore, an exponential equilibration result is proved for sufficiently small Lipschitz constants of the noise by using the relative Rao entropy. Numerical tests illustrate the behavior of solutions in one space dimension for two and three population species.

math.AP↗

arXiv2022

Landau-Lifshitz-Gilbert equations: Controllability by Low Modes Forcing for deterministic version and Support Theorems for Stochastic version

In this article, we study the controllability issues of the Landau-Lifshitz-Gilbert Equations (LLGEs), accompanied with non-zero exchange energy only, in an interval in one spatial dimension with Neumann boundary conditions. The paper is of twofold. In the first part of the paper, we study the controllability issues of the LLGEs. The control force acting here is degenerate i.e., it acts through a few numbers of low mode frequencies. We exploit the Fourier series expansion of the solution. We borrow methods of differential geometric control theory (Lie bracket generating property) to establish the global controllability of the finite-dimensional Galerkin approximations of LLGEs. We show $L^2$ approximate controllability of the full system. In the second part, we consider the LLGEs with lower-dimensional degenerate random forcing (finite-dimensional Brownian motions) and study support theorems.

math.OC↗