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Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
We consider a $4\times4$ nonlinear reaction-diffusion system posed on a smooth domain $\Omega$ of $\mathbb{R}^N$ ($N \geq 1$) with controls localized in some arbitrary nonempty open subset $\omega$ of the domain $\Omega$. This system is a…
In this article, we prove the (uniform) global exponential stabilization of the cubic defocusing Schr\"odinger equation on the torus d-dimensional torus, for d=1, 2 or 3, with a linear damping localized in a subset of the torus satisfying…
The current paper is concerned with the stabilization in the following parabolic-parabolic-elliptic chemotaxis system with singular sensitivity and Lotka-Volterra competitive kinetics, \begin{equation} \begin{cases} u_t=\Delta u-\chi_1…
Understanding the non-equilibrium dynamics of quantum many-body systems remains one of the grand challenges of modern physics. In particular, increasing attention has been devoted to the emergence of non-equilibrium universality classes…
Predictor-based stabilization results are provided for nonlinear systems with input delays and a compact absorbing set. The control scheme consists of an inter-sample predictor, a global observer, an approximate predictor, and a nominal…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
In this paper we use the homotopy invariants methods to study the global dynamics of the reaction-diffusion systems that are at resonance at infinity. Considering degrees of the resonance for the nonlinear perturbation we establish…
The interplay of strong interaction and strong disorder, as contained in the Anderson-Hubbard model, is addressed using two non-perturbative numerical methods: the Lanczos algorithm in the grand canonical ensemble at zero temperature and…
Motivated by a low-energy effective description of gauge theory/string theory duality, we conjecture that the dynamics of $SO(4)$-invariant states in a large class of four-dimensional conformal gauge theories on $S^3$ with non-equal central…
In this paper we show the lower semicontinuity of the global attractors of autonomous thermoelastic plate systems with Neumann boundary conditions when some reaction terms are concentrated in a neighborhood of the boundary and this…
In this paper we demonstrate the feasibility and utility of an augmented version of the Gibbs ensemble Monte Carlo method for computing the phase behavior of systems with strong, extremely short-ranged attractions. For generic potential…
We analyze semilinear reaction-diffusion systems that are mass controlled, and have nonlinearities that satisfy critical growth rates. The systems under consideration are only assumed to satisfy natural assumptions, namely the preservation…
This paper addresses the topic of global output feedback stabilization of semilinear reaction-diffusion PDEs. The semilinearity is assumed to be confined into a sector condition. We consider two different types of actuation configurations,…
The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential attractor and the stabilization of the zero steady state…
Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and…
We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin…
All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…
We consider the quantum reaction-diffusion dynamics in $d$ spatial dimensions of a Fermi gas subject to binary annihilation reactions $A+A \to \emptyset$. These systems display collective nonequilibrium long-time behavior, which is…
The kinetics of encounter-controlled processes in growing domains is markedly different from that in a static domain. Here, we consider the specific example of diffusion limited coalescence and annihilation reactions in one-dimensional…