arXiv subjects

Jawad Salhi

Publications and source records attributed to Jawad Salhi.

7 recordsLinked to original sources

arXiv2026

Long-Time Stability Analysis for Stochastic Evolution Equations with Multiplicative Noise

In this paper, we study the long-time stability behavior of a class of linear stochastic evolution equations in a Hilbert space with multiplicative noise. Explicit sufficient conditions for $p$-th moment and almost sure exponential stability are established, highlighting the interplay between the principal eigenvalue of the governing operator, the drift coefficient, and the noise intensity. The relationship between these two notions of stability is also clarified. Applications to several stochastic partial differential equations are presented. In addition, a fully discrete spectral Galerkin method together with the implicit Euler--Maruyama scheme is shown to preserve these stability properties at the discrete level. Finally, numerical simulations are provided to confirm the theoretical results.

math.AP↗

arXiv2026

A degenerate reaction-diffusion SIR model in interconnected regions

This paper presents a novel time-space SIR (Susceptible-Infected-Recovered) model for simulating infectious disease dynamics in two interconnected regions. The model is formulated as a coupled reaction-diffusion system with boundary conditions that dynamically switch from Robin to Neumann types, effectively modelling policy-driven interventions such as lockdowns. A key innovation lies in the incorporation of degenerate diffusion, arising from vanishing population density, which significantly influences transmission behaviour near regional borders. The wellposedness of the model is rigorously established using the Faedo-Galerkin method, ensuring the existence, uniqueness, and positivity of weak solutions. Numerical simulations, performed using the Finite Volume Method, validate the theoretical findings and demonstrate the impact of migration and mobility restrictions on epidemic progression. This framework offers valuable insights for understanding and controlling disease spread in spatially heterogeneous and interconnected settings.

math.AP↗

arXiv2025

Indirect stabilization of nonlinear coupled wave equations in the presence of time delay or indefinite damping

This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other experiences a discrete time delay. By reformulating the problem in an abstract framework, we use semigroup theory and energy methods to establish well-posedness and derive conditions that guarantee exponential energy decay. In the second case, we examine a scenario where a frictional damping term appears in the first equation, while the second equation contains an indefinite damping term, namely with a sign-changing coefficient. Although this setup can be viewed as a special case of the first, we analyze it separately and show that exponential stability still holds under a weaker condition.

math.AP↗

arXiv2024

Theoretical and numerical indirect stabilization of coupled wave equations with a single time-delayed damping

The focal point of this paper is to theoretically investigate and numerically validate the effect of time delay on the exponential stabilization of a class of coupled hyperbolic systems with delayed and non-delayed dampings. The class in question consists of two strongly coupled wave equations featuring a delayed and non-delayed damping terms on the first wave equation. Through a standard change of variables and semi-group theory, we address the well-posedness of the considered coupled system. Thereon, based on some observability inequalities, we derive sufficient conditions guaranteeing the exponential decay of a suitable energy. On the other hand, from the numerical point of view, we validate the theoretical results in $1D$ domains based on a suitable numerical approximation obtained through the Finite Difference Method. More precisely, we construct a discrete numerical scheme which preserves the energy decay property of its continuous counterpart. Our theoretical analysis and implementation of our developed numerical scheme assert the effect of the time-delayed damping on the exponential stability of strongly coupled wave equations.

math.OC↗

arXiv2021

Boundary controllability for a degenerate and singular wave equation

In this paper, we deal with the boundary controllability of a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. Exact boundary controllability is proved in the range of subcritical/critical potentials and for sufficiently large time, through a boundary controller acting away from the degenerate/singular point. By duality argument, we reduce the problem to an observability estimate for the corresponding adjoint system, which is proved by means of the multiplier method and a new special Hardy-type inequality.

math.OC↗

arXiv2021

Boundary controllability for a coupled system of degenerate/singular parabolic equations

In this paper we study the boundary controllability for a system of two coupled degenerate/singular parabolic equations with a control acting on only one equation. We analyze both approximate and null boundary controllability properties. Besides, we provide an estimate on the null-control cost. The proofs are based on the use of the moment method by Fattorini and Russell together with some results on biorthogonal families.

math.OC↗

arXiv2020

Null controllability for the singular heat equation with a memory term

In this paper we focus on the null controllability problem for the heat equation with the so-called inverse square potential and a memory term. To this aim, we first establish the null controllability for a nonhomogeneous singular heat equation by a new Carleman inequality with weights which do not blow up at t=0. Then the null controllability property is proved for the singular heat equation with memory under a condition on the kernel, by means of Kakutani's fixed-point Theorem.

math.AP↗