Related papers: Uniform convergence of operator semigroups without…

In this article we study a class of hyperbolic partial differential equations of order one on the semi-axis. The so-called port-Hamiltonian systems cover for instance the wave equation and the transport equation, but also networks of the…

This paper investigates the controllability of systems governed by conformable fractional order derivatives. It first establishes the existence and uniqueness of evolution operators for non-autonomous fractional-order homogeneous systems,…

In this paper we present an efficient numerical approach based on the Renormalization Group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time asymptotic behavior of solutions to nonlinear…

We present a novel approach to the analysis of regularity and decay for solutions of wave equations in a neighborhood of null infinity in asymptotically flat spacetimes of any dimension. The classes of metrics and wave type operators we…

This paper deals with the approximation of the spectrum of linear and nonautonomous delay differential equations through the reduction of the relevant evolution semigroup from infinite to finite dimension. The focus is placed on classic…

Let $(-\Delta)_c^s$ be the realization of the fractional Laplace operator on the space of continuous functions $C_0(\mathbb{R})$, and let $(-\Delta_h)^s$ denote the discrete fractional Laplacian on $C_0(\mathbb{Z}_h)$, where $0<s<1$ and…

A famous result by Jeavons, Cohen, and Gyssens shows that every constraint satisfaction problem (CSP) where the constraints are preserved by a semi-lattice operation can be solved in polynomial time. This is one of the basic facts for the…

We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…

This paper is to study some conditions on semigroups, generated by some class of non-densely defined operators in the closure of its domain, in order that certain bounded perturbations preserve some regularity properties of the semigroup…

In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can…

This article deals with the study of a non-local one-dimensional quasilinear problem with continuous forcing. We use a time-reparameterization to obtain a semilinear problem and study a more general equation using semigroup theory. The…

We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of…

If the semigroup is slowly non-dissipative, i.e., its solutions can diverge to infinity as time tends to infinity, one still can study its dynamics via the approach by the unbounded attractors - the counterpart of the classical notion of…

We study continuity and equicontinuity of semigroups on norming dual pairs with respect to topologies defined in terms of the duality. In particular, we address the question whether continuity of a semigroup already implies (local/quasi)…

We develop the regularity theory for solutions to space-time nonlocal equations driven by fractional powers of the heat operator $$(\partial_t-\Delta)^su(t,x)=f(t,x),\quad\hbox{for}~0<s<1.$$ This nonlocal equation of order $s$ in time and…

In a recent paper we presented a general perturbation result for generators of $C_0$-semigroups. The aim of the present paper is to replace, in case the unperturbed semigroup is analytic, the various conditions appearing in this result by…

We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the…

We study linear operators $T$ on Banach spaces for which there exists a $C_0$-semigroup $(T(t))_{t\geq 0}$ such that $T=T(1)$. We present a necessary condition in terms of the spectral value 0 and give classes of examples where this can or…

We introduce a comprehensive framework for subordinacy theory applicable to long-range operators on $\ell^2(\mathbb Z)$, bridging dynamical systems and spectral analysis. For finite-range operators, we establish a correspondence between the…

We investigate a class of nonlocal conservation laws in several space dimensions, where the continuum average of weighted nonlocal interactions are considered over a finite horizon. We establish well-posedness for a broad class of flux…