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Uniqueness is proven for two 3-d inverse problems of the determination of the spatially distributed sound speed in the frequency dependent acoustic PDE. The main new point is the assumption that only the modulus of the scattered complex…
We generalize the theory of periodic homogenization for multidimensional SDEs with additive Brownian and stable L\'evy noise for $\alpha\in (1,2)$ to the setting of singular periodic Besov drifts of regularity $\beta\in ((2-2\alpha)/3,0)$…
Stabilization of a coupled system consisting of a parabolic partial differential equation and an elliptic partial differential equation is considered. Even in the situation when the parabolic equation is exponentially stable on its own, the…
Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…
The study of resonances (and well-posedness) for complex systems under time-periodic loading is of broad interest in application. The work of Galdi et al.~(2014) connects asymptotic stability of solutions to an unforced Cauchy problem to…
In this work, we address a parabolic problem featuring a potentially doubly nonlinear term, governed by a combination of local and nonlocal operators (see Problem P1 below). We first establish the local existence of weak energy solutions…
For the linearized reconstruction problem in Electrical Impedance Tomography (EIT) with the Complete Electrode Model (CEM), Lechleiter and Rieder (2008 Inverse Problems 24 065009) have shown that a piecewise polynomial conductivity on a…
We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice $\mathbb{Z}$. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively.…
Various controllability conditions have been obtained by researchers for heterogeneous networked systems with linear dynamics. However, the literature for nonlinear, heterogeneous networked systems is comparatively less. In this paper we…
This paper studies the exponential stability of primal-dual gradient dynamics (PDGD) for solving convex optimization problems where constraints are in the form of Ax+By= d and the objective is min f(x)+g(y) with strongly convex smooth f but…
We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone operator into the closed convex hull of its single-valued part…
In our work we study non-variational, nonlinear singularly perturbed elliptic models enjoying a double degeneracy character with prescribed boundary value in a domain. In such a scenario, we establish the existence of solutions. We also…
This paper is composed of two parts. In the first part we consider McKean-Vlasov Partial Differential Equations (PDEs), obtained as thermodynamic limits of interacting particle systems (i.e. in the limit $N\to\infty$, where N is the number…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
We present an optimization-based framework for analysis and control of linear parabolic partial differential equations (PDEs) with spatially varying coefficients without discretization or numerical approximation. For controller synthesis,…
We are concerned with the problem of determining the damping boundary coefficient appearing in a dissipative wave equation from a single boundary measurement. We prove that the uniqueness holds at the origin provided that the initial…
We show that if a linear infinite-dimensional system is exponentially stabilizable by compact feedback, it is also stabilizable by means of a sampled-data feedback that is fed through a globally Lipschitz nonlinearity, provided that the…
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…
This paper develops systematically the output feedback exponential stabilization for a one-dimensional unstable/anti-stable wave equation where the control boundary suffers from both internal nonlinear uncertainty and external disturbance.…