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Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
We consider a system of reaction-diffusion equations in a bounded interval of the real line, with emphasis on the metastable dynamics, whereby the time-dependent solution approaches its steady state in an asymptotically exponentially long…
We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system,…
A class of coupled time-space fractional reaction-diffusion systems derived from reversible chemical reactions over a bounded domain is investigated. Employing mainly an appropriate Lyapunov functional and an improved maximum principle, we…
Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between…
We consider a nonlinear parabolic model that forces solutions to stay on a $L^2$-sphere through a nonlocal term in the equation. We study the local and global well-posedness on a bounded domain and the whole Euclidean space in the energy…
In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…
The theory of slow-fast gradient systems leads in a natural way to non-equilibrium steady states, because on the slow time scale the fast subsystem stays in steady states that are controlled by the interaction with the slow system. Using…
The mass-based Maxwell-Stefan approach to one-phase multicomponent reactive mixtures is mathematically analyzed. It is shown that the resulting quasilinear, strongly coupled reaction-diffusion system is locally well-posed in an…
Hamiltonian systems with long-range interactions give rise to long lived out of equilibrium macroscopic states, so-called quasi-stationary states. We show here that, in a suitably generalized form, this result remains valid for many such…
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…
In this paper, we consider a time-fractional reaction-diffusion system with the same nonlinearities of the Newton-Leipnik chaotic system. Through analytical tools and numerical results, we derive sufficient conditions for the asymptotic…
This work focuses on stability of regime-switching diffusions consisting of continuous and discrete components, in which the discrete component switches in a countably infinite set and its switching rates at current time depend on the…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…