Related papers: Backward Uniqueness for Coupled Ultraparabolic Ope…
We study the behaviour of solutions to a class of nonlinear degenerate parabolic problems when the data are perturbed. The class includes the Richards equation, Stefan problem and the parabolic $p$-Laplace equation. We show that, up to a…
Most of the rigid-body systems which evolve on nonlinear Lie groups where Euclidean control designs lose geometric meaning. In this paper, we introduce a log-linear backstepping control law on SE2(3) that preserves full…
We investigate the convergence rate for the time discretization of a class of quadratic backward SDEs -- potentially involving path-dependent terminal values -- when coupled with non-standard Lipschitz-type forward SDEs. In our review of…
In application of the complex Langevin method to QCD at high density and low temperature, the singular-drift problem occurs due to the appearance of near-zero eigenvalues of the Dirac operator. In order to avoid this problem, we proposed to…
We consider systems of parabolic equations coupled in zero order terms in a star-like or a tree-like shape, with an internal control acting in only one of the equations. We obtain local exact controllability to the stationary solutions of…
We obtain an existence and uniqueness theorem for fully coupled forward-backward SDEs (FBSDEs) with jumps via the classical solution to the associated quasilinear parabolic partial integro-differential equation (PIDE), and provide the…
We consider the inverse problem of identification of degenerate diffusion coefficient of the form $x^\alpha a(x)$ in a one dimensional parabolic equation by some extra data. We first prove by energy methods the uniqueness and Lipschitz…
We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point,…
In this paper, we continue our study on a general time-inconsistent stochastic linear--quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of…
The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998, based on Carleman estimates, seems hard to apply to the case of Grushin-type operators of interest to this paper. Indeed,…
We study parabolic equations governed by integro-differential operators with nonlocal components in some directions and local components in the remaining directions. The setting contains the purely nonlocal, as well as the purely local…
The Koopman and Perron Frobenius transport operators are fundamentally changing how we approach dynamical systems, providing linear representations for even strongly nonlinear dynamics. Although there is tremendous potential benefit of such…
In this article, we present a novel Carleman estimate for ultrahyperbolic operators, in $ \mathbb{R}^m_t \times \mathbb{R}^n_x $. Then, we use a special case of this estimate to obtain improved observability results for wave equations with…
In this work, we establish the so-called backward uniqiueness property for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow…
While for coupled hyperbolic PDEs of first order there now exist numerous PDE backstepping designs, systems with zero speed, i.e., without convection but involving infinite-dimensional ODEs, which arise in many applications, from…
This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain in R^N, we consider a system…
By using some deep tools from microlocal analysis, J. Le Rousseau and L. Robbiano (Invent. Math., 183 (2011), 245--336) established several Carleman estimates for parabolic operators with isotropic diffusion coefficients which have jumps at…
An instructive example is presented to elucidate the mathematical situation in the non-uniqueness problem of the infinite Friedmann-Keller hierarchy of equations for all multi-point moments within the theory of spatially unbounded…
The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…
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…