Related papers: Control estimates for 0th order pseudodifferential…
We investigate the effect of small diffusion on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors of the principal eigenvalues, as…
Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic…
This paper addresses an optimal control problem governed by a rate independent evolution involving an integral operator. Its particular feature is that the dissipation potential depends on the history of the state. Because of the non-smooth…
We study a damped semi-linear wave equation in a bounded domain with smooth boundary. It is proved that any sufficiently smooth solution can be stabilised locally by a finite-dimensional feedback control supported by a given open subset…
We obtain necessary optimality conditions for a semi-discretized optimal control problem for the classical system of nonlinear partial differential equations modelling the water-oil (isothermal dead-oil model).
In \cite{LPP:2025}, it was shown that, in arbitrary dimension, the spatial semi-discretization of a controlled stochastic parabolic operator is generically not null-controllable. Nevertheless, $\phi$-null controllability results remain…
We prove observability and null-controllability for quadratic parabolic differential equations. The sensor set is allowed to be sparse and have finite volume if the generator has trivial singular space $S$. In the case of generators with…
In this study, we study the null controllability of a multi-dimensional degenerate parabolic equation characterized by a degenerate interior point. The control domain, which is an arbitrary inner region, does not encompass the degenerate…
An analysis of necessary conditions for the existence of controlled dynamics with an attractor of a specified topological type is given. It uses the Hopf classification by degree for Gauss maps of manifolds to spheres of the same dimension,…
We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form $\alpha/x$, $\alpha>0$. We establish the exponential stability of the semigroup for all…
This research delves into the exact controllability of semilinear measure-driven integrodifferential systems in nonlocal settings. We provide sufficient controllability requirements using the measure of noncompactness and the M\"onch fixed…
Existence of optimal solutions and necessary optimality conditions for a controlled version of Moreau's sweeping process are derived. The control is a measurable ingredient of the dynamics and the constraint set is a polyhedron. The novelty…
We study the null controllability for a degenerate/singular wave equation with drift in non divergence form. In particular, considering a control localized on the non degenerate boundary point, we provide some conditions for the boundary…
In this paper we consider semilinear wave equation and other second order $\sigma$-evolution equations with different (effective or non-effective) damping mechanisms driven by fractional Laplace operators; in particular, the nonlinear term…
We prove existence and conditional energetic stability of solitary-wave solutions for the two classes of pseudodifferential equations $ u_t+\left(f(u)\right)_x-\left(L u\right)_x=0 $ and $ u_t+\left(f(u)\right)_x+\left(L u\right)_t=0, $…
We consider a degenerate/singular wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a…
We define and study classes of smooth functions which are less regular than Gevrey functions. To that end we introduce two-parameter dependent sequences which do not satisfy Komatsu's condition (M.2)', which implies stability under…
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a…
We consider boundary value problems for 1D autonomous damped and delayed semilinear wave equations of the type $$ \partial^2_t u(t,x)- a(x,\lambda)^2\partial_x^2u(t,x)= b(x,\lambda,u(t,x),u(t-\tau,x),\partial_tu(t,x),\partial_xu(t,x)), \; x…
The aim of this paper is to derive a maximum principle for a control problem governed by a stochastic partial differential equation (SPDE) with locally monotone coefficients. In particular, necessary conditions for optimality for this…