Related papers: On local solutions to time-varying linear DAEs
Utilising the notion of measures of non-compactness and Kamke function of order $\alpha$, we address the question of solvability of fractional differential equations in Banach spaces. In particular, we provide sufficient conditions ensuring…
In this paper we show the unexpected property that extension from local to global without loss of regularity holds for the solutions of a wide class of vector-valued differential equations, in particular for the class of fractional abstract…
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage…
A generalization of the Euler's elastic problem, i.e., finding a stationary configuration (planar elastica) of the Bernoulli's thin ideal elastic rod with boundary conditions defined through fixed endpoints and/or tangents at the endpoints,…
The paper deals with the controllability properties of the Kawahara equation posed on a periodic domain. We show that the equation is exactly controllable by means of a control depending only on time and acting on the system through a given…
Local versions of measurability have been around for a long time. Roughly, one splits the notion of $\mu $-completeness into pieces, and asks for a uniform ultrafilter over $\mu $ satisfying just some piece of $\mu $-completeness. Analogue…
In this paper, we establish a local theory, i.e., existence, uniqueness and blow-up criterion, for a general family of singular SDEs in some Hilbert space. The key requirement is an approximation property that allows us to embed the…
We consider the 1D nonlinear Schr\"odinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground state has been proved by Beauchard and Laurent in…
It is now well understood that equations of viscoelasticity can be seen as perturbation of wave type equations. This observation can be exploited in several different ways and it turns out that it is a usefull tool when studying…
In this paper, a weak Local Linearization scheme for Stochastic Differential Equations (SDEs) with multiplicative noise is introduced. First, for a time discretization, the solution of the SDE is locally approximated by the solution of the…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
We introduce the Local Increasing Regularity Method (LIRM) which allows us to get from \emph{local} a priori estimates, on solutions $u$ of a linear equation $\displaystyle Du=\omega ,$ \emph{global} ones. As an application we shall prove…
We consider a class of elliptic and parabolic problems, featuring a specific nonlocal operator of fractional-laplacian type, where integration is taken on variable domains. Both elliptic and parabolic problems are proved to be uniquely…
We consider Schr\"odinger PDEs, posed on a boundaryless Riemannian manifold $M$, with bilinear control. We propose a new method to prove the global $L^2$-approximate controllability. Contrarily to previous ones, it works in arbitrarily…
This work extends local linear regression to Banach space-valued time series for estimating smoothly varying means and their derivatives in non-stationary data. The asymptotic properties of both the standard and bias-reduced Jackknife…
The existence of solutions to the boundary tracking of the displacement at one end of a linear Timoshenko beam is discussed on the basis of the Cauchy problem with time and space interchanged.
We consider a linear Korteweg-de Vries equation on a bounded domain with a left Dirichlet boundary control.The controllability to the trajectories of such a system was proved in the last decade by using Carleman estimates.Here, we go a step…
Time-varying non-convex continuous-valued non-linear constrained optimization is a fundamental problem. We study conditions wherein a momentum-like regularising term allow for the tracking of local optima by considering an ordinary…
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…
This paper investigates full stability properties for \emph{variational Nash equilibriums} of a system of parametric nonconvex optimal control problems governed by semilinear elliptic partial differential equations. We first obtain some new…