Related papers: Concentration around a stable equilibrium for the …
In this paper we study the existence and uniqueness of Nash equilibria (solution to competition-wise problems, with several controls trying to reach possibly different goals) associated to linear partial differential equations and show…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…
We study nonlinear stability of pulled fronts in scalar parabolic equations on the real line of arbitrary order, under conceptual assumptions on existence and spectral stability of fronts. In this general setting, we establish sharp…
This work concerns the exponential stabilization of underactuated linear homogeneous systems of m parabolic partial differential equations (PDEs) in cascade (reaction-diffusion systems), where only the first state is controlled either…
We prove that the tail probabilities of sums of independent uniform random variables, up to a multiplicative constant, are dominated by the Gaussian tail with matching variance and find the sharp constant for such stochastic domination.
This work is devoted to the stabilization of parabolic systems with a finite-dimensional control subjected to a constant delay. Our main result shows that the Fattorini-Hautus criterion yields the existence of such a feedback control, as in…
This work investigates the existence and uniqueness of the Nash equilibrium (solutions to competitive problems in which individual controls aim at separate desired states) for a bi-objective optimal control problem governed by a fractional…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…
We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This…
The problem of stabilization of unstable periodic orbits of discrete nonlinear systems is considered in the article. A new generalization of the delayed feedback, which solves the stabilization problem, is proposed. The feedback is…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
Systems of non-autonomous parabolic partial differential equations over a bounded domain with nonlinear term of Carath\'eodory type are considered. Appropriate topologies on sets of Lipschitz Carath\'eodory maps are defined in order to have…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…
In this note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions' Lemma for deterministic problems,…
In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…
We study the fully discrete elliptic integrable model Q4 and its immediate trigonometric and rational counterparts (Q3, Q2 and Q1). Singular boundary problems for these equations are systematised in the framework of global singularity…