Manil T. Mohan
YOU?
Author Swipe
View article: Finite element analysis of a nonlinear heat Equation with damping and pumping effects
Finite element analysis of a nonlinear heat Equation with damping and pumping effects Open
We study the following nonlinear heat equation with damping and pumping effects (a reaction-diffusion equation) posed on a bounded simply connected convex domain $Ω\subset \mathbb{R}^d$, $d \geq 1$ with Lipschitz boundary $\partialΩ$: $$ \…
View article: Large deviation principle for a stochastic nonlinear damped Schrodinger equation
Large deviation principle for a stochastic nonlinear damped Schrodinger equation Open
The present paper focuses on the stochastic nonlinear Schrodinger equation with polynomial nonlinearity, and a zero-order (no derivatives involved) linear damping. Here, the random forcing term appears as a mix of a nonlinear noise in the …
View article: A viscosity solution approach to the large deviation principle for stochastic convective Brinkman-Forchheimer equations
A viscosity solution approach to the large deviation principle for stochastic convective Brinkman-Forchheimer equations Open
This article develops the viscosity solution approach to the large deviation principle for the following two- and three-dimensional stochastic convective Brinkman-Forchheimer equations on the torus $\mathbb{T}^d,\ d\in\{2,3\}$ with small n…
View article: The $$\mathbb {H}^1$$-compact global attractor for the two-dimensional Oldroyd fluid flow equations in bounded domains
The $$\mathbb {H}^1$$-compact global attractor for the two-dimensional Oldroyd fluid flow equations in bounded domains Open
View article: Global well-posedness and Asymptotic analysis of a nonlinear heat equation with constraints of finite codimension
Global well-posedness and Asymptotic analysis of a nonlinear heat equation with constraints of finite codimension Open
We prove the global existence and the uniqueness of the $L^p\cap H_0^1-$valued ($2\leq p < \infty$) strong solutions of a nonlinear heat equation with constraints over bounded domains in any dimension $d\geq 1$. Along with the \textit{Faed…
View article: Feedback Stabilizability of a generalized Burgers-Huxley equation with kernel around a non-constant steady state
Feedback Stabilizability of a generalized Burgers-Huxley equation with kernel around a non-constant steady state Open
In this article, we investigate a generalized Burgers-Huxley equation with a smooth kernel defined in a bounded domain $Ω\subset\mathbb{R}^d$, $d\in\{1,2,3\}$, focusing on feedback stabilizability around a non-constant steady state. Initia…
View article: Error estimates for viscous Burgers' equation using deep learning method
Error estimates for viscous Burgers' equation using deep learning method Open
The article focuses on error estimates as well as stability analysis of deep learning methods for stationary and non-stationary viscous Burgers equation in two and three dimensions. The local well-posedness of homogeneous boundary value pr…
View article: Stabilizability of 2D and 3D Navier-Stokes equations with memory around a non-constant steady state
Stabilizability of 2D and 3D Navier-Stokes equations with memory around a non-constant steady state Open
In this article, we investigate the stabilizability of the two- and three-dimensional Navier-Stokes equations with memory effects around a non-constant steady state using a localized interior control. The system is first linearized around …
View article: Boundary control of generalized Korteweg-de Vries-Burgers-Huxley equation: Well-posedness, stabilization and numerical studies
Boundary control of generalized Korteweg-de Vries-Burgers-Huxley equation: Well-posedness, stabilization and numerical studies Open
View article: Kolmogorov equations for 2D stochastic convective Brinkman-Forchheimer equations: Analysis and Applications
Kolmogorov equations for 2D stochastic convective Brinkman-Forchheimer equations: Analysis and Applications Open
In this work, we consider the following 2D stochastic convective Brinkman-Forchheimer (SCBF) equations in a bounded smooth domain $\mathcal{O}$: \begin{align*} \mathrm{d}\boldsymbol{u}+\left[-μΔ\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\bo…
View article: On the convective Brinkman-Forchheimer equations
On the convective Brinkman-Forchheimer equations Open
The convective Brinkman--Forchheimer equations or the Navier--Stokes equations with damping in bounded or periodic domains $\subset\mathbb{R}^d$, $2\leq d\leq 4$ are considered in this work. The existence and uniqueness of a global weak so…
View article: Well-posedness of three-dimensional Damped Cahn-Hilliard-Navier-Stokes Equations
Well-posedness of three-dimensional Damped Cahn-Hilliard-Navier-Stokes Equations Open
This paper presents a mathematical analysis of the evolution of a mixture of two incompressible, isothermal fluids flowing through a porous medium in a three dimensional bounded domain. The model is governed by a coupled system of convecti…
View article: Random dynamics of solutions for three-dimensional stochastic globally modified Navier-Stokes equations on unbounded Poincaré domains
Random dynamics of solutions for three-dimensional stochastic globally modified Navier-Stokes equations on unbounded Poincaré domains Open
In this article, we consider a novel version of three-dimensional (3D) globally modified Navier-Stokes (GMNS) system introduced by [Caraballo et. al., Adv. Nonlinear Stud. (2006), 6:411-436], which is very significant from the perspective …
View article: Central limit theorem and moderate deviation principle for the stochastic generalized Burgers-Huxley equation with multiplicative noise
Central limit theorem and moderate deviation principle for the stochastic generalized Burgers-Huxley equation with multiplicative noise Open
In this work, we investigate the Central Limit Theorem (CLT) and Moderate Deviation Principle (MDP) for the stochastic generalized Burgers-Huxley (SGBH) equation with multiplicative Gaussian noise. The SGBH equation is a diffusion-convecti…
View article: Existence and asymptotic autonomous robustness of random attractors for three-dimensional stochastic globally modified Navier-Stokes equations on unbounded domains
Existence and asymptotic autonomous robustness of random attractors for three-dimensional stochastic globally modified Navier-Stokes equations on unbounded domains Open
In this article, we discuss the existence and asymptotically autonomous robustness (AAR) (almost surely) of random attractors for 3D stochastic globally modified Navier-Stokes equations (SGMNSE) on Poincaré domains (which may be bounded or…
View article: Dynamic programming of the stochastic 2D-Navier-Stokes equations forced by Lévy noise
Dynamic programming of the stochastic 2D-Navier-Stokes equations forced by Lévy noise Open
View article: Blow-up of stochastic semilinear parabolic equations driven by Lévy noise
Blow-up of stochastic semilinear parabolic equations driven by Lévy noise Open
The blow-up phenomena of stochastic semilinear parabolic equations with additive as well as linear multiplicative Lévy noises are investigated in this work. By suitably modifying the concavity method in the stochastic context, we establish…
View article: Non-Conforming Structure Preserving Finite Element Method for Doubly Diffusive Flows on Bounded Lipschitz Domains
Non-Conforming Structure Preserving Finite Element Method for Doubly Diffusive Flows on Bounded Lipschitz Domains Open
We study a stationary model of doubly diffusive flows with temperature-dependent viscosity on bounded Lipschitz domains in two and three dimensions. A new well-posedness and regularity analysis of weak solutions under minimal assumptions o…
View article: Existence and uniqueness of weak solutions for the generalized stochastic Navier-Stokes-Voigt equations
Existence and uniqueness of weak solutions for the generalized stochastic Navier-Stokes-Voigt equations Open
In this work, we consider the incompressible generalized Navier-Stokes-Voigt equations in a bounded domain $\mathcal{O}\subset\mathbb{R}^d$, $d\geq 2$, driven by a multiplicative Gaussian noise. The considered momentum equation is given by…
View article: Local exact controllability to the trajectories of the convective Brinkman-Forchheimer equations
Local exact controllability to the trajectories of the convective Brinkman-Forchheimer equations Open
In this article, we discuss the local exact controllability to trajectories of the following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) defined in a bounded domain $Ω \subset\mathbb{R}^d$ ($d=2,3$) …
View article: Boundary control of generalized Korteweg-de Vries-Burgers-Huxley equation: Well-Posedness, Stabilization and Numerical Studies
Boundary control of generalized Korteweg-de Vries-Burgers-Huxley equation: Well-Posedness, Stabilization and Numerical Studies Open
A boundary control problem for the following generalized Korteweg-de Vries-Burgers-Huxley equation: $$u_t=νu_{xx}-μu_{xxx}-αu^δu_x+βu(1-u^δ)(u^δ-γ), \ x\in[0,1], \ t>0,$$ where $ν,μ,α,β>0,$ $δ\in[1,\infty)$, $γ\in(0,1)$ subject to Neumann …
View article: Approximate controllability of non-autonomous second order impulsive functional evolution equations in Banach spaces.
Approximate controllability of non-autonomous second order impulsive functional evolution equations in Banach spaces. Open
This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss the approximate controllability of seco…
View article: Lower and upper bounds for the explosion times of a system of semilinear SPDEs
Lower and upper bounds for the explosion times of a system of semilinear SPDEs Open
In this paper, we obtain lower and upper bounds for the blow-up times to a system of semilinear stochastic partial differential equations given by du=[(Δ+V)u(t,x)+u(t,x)+u(t,x)]dt+ku(t,x)dW du=[(Δ+V)u(t,x)+u(t,x)+u(t,x)]dt+ku(t,x)dW where …
View article: Global Existence and Non-Existence of Weak Solutions for Non-Local Stochastic Semilinear Reaction-Diffusion Equations Driven by a Fractional Noise
Global Existence and Non-Existence of Weak Solutions for Non-Local Stochastic Semilinear Reaction-Diffusion Equations Driven by a Fractional Noise Open
View article: An inverse source problem for convective Brinkman-Forchheimer equations with the final overdetermination
An inverse source problem for convective Brinkman-Forchheimer equations with the final overdetermination Open
In this paper, we examine an inverse problem for the following convective Brinkman-Forchheimer (CBF) equations or damped Navier-Stokes equations:$ \begin{align*} \boldsymbol{v}_t-\mu \Delta\boldsymbol{v}+(\boldsymbol{v}\cdot\nabla)\boldsym…
View article: Feedback stabilization of Convective Brinkman-Forchheimer Extended Darcy equations
Feedback stabilization of Convective Brinkman-Forchheimer Extended Darcy equations Open
In this article, the following controlled convective Brinkman-Forchheimer extended Darcy (CBFeD) system is considered in a $d$-dimensional torus: \begin{align*} \frac{\partial\boldsymbol{y}}{\partial t}-μΔ\boldsymbol{y}+(\boldsymbol{y}\cdo…
View article: Analysis and Numerical Study of Boundary control of generalized Burgers-Huxley equation
Analysis and Numerical Study of Boundary control of generalized Burgers-Huxley equation Open
In this work, a boundary control problem for the following generalized Burgers-Huxley (GBH) equation: $$u_t=νu_{xx}-αu^δu_x+βu(1-u^δ)(u^δ-γ), $$ where $ν,α,β>0,$ $1\leqδ<\infty$, $γ\in(0,1)$ subject to Neumann boundary conditions is analyz…
View article: Global existence and non-existence of weak solutions for non-local stochastic semilinear reaction-diffusion equations driven by a fractional noise
Global existence and non-existence of weak solutions for non-local stochastic semilinear reaction-diffusion equations driven by a fractional noise Open
In the present paper, we study the existence and blow-up behavior to the following stochastic non-local reaction-diffusion equation: \begin{equation*} \left\{ \begin{aligned} du(t,x)&=\left[(Δ+γ) u(t,x)+\int_{D}u^{q}(t,y)dy -ku^{p}(t,x)+δu…
View article: Random attractors and invariant measures for stochastic convective Brinkman-Forchheimer equations on 2D and 3D unbounded domains
Random attractors and invariant measures for stochastic convective Brinkman-Forchheimer equations on 2D and 3D unbounded domains Open
In this work, we consider the 2D and 3D SCBF equations driven by irregular additive white noise$ \mathrm{d}\boldsymbol{u}-[\mu \Delta\boldsymbol{u}-(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}-\alpha\boldsymbol{u}-\beta|\boldsymbol{u}|^{r-1}\…
View article: 2D and 3D convective Brinkman-Forchheimer equations perturbed by a subdifferential and applications to control problems
2D and 3D convective Brinkman-Forchheimer equations perturbed by a subdifferential and applications to control problems Open
The following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) with potential$ \begin{equation*} \frac{\partial \boldsymbol{y}}{\partial t}-\mu \Delta\boldsymbol{y}+(\boldsymbol{y}\cdot\nabla)\boldsymbol{…