Related papers: Carleman Estimates for Parabolic Operators with Di…
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…
We prove a Carleman estimate for elliptic second order partial differential operators with Lipschitz continuous coefficients. The Carleman estimate is valid for any complex-valued function $u\in W^{2,2}$ with support in a punctured ball of…
The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used…
A Carleman estimate and the unique continuation of solutions for an anomalous diffusion equation with fractional time derivative of order $0<\alpha<1$ are given. The estimate is derived via some subelliptic estimate for an operator…
We will show that the same type of estimates known for the fundamental solutions for scalar parabolic equations with smooth enough coefficients hold for the first order derivatives of fundamental solution with respect to space variables of…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in spatial variables and random stationary in time. Under proper mixing assumptions, we study the limit behaviour of the…
The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a…
In this article, we investigate the Calder\'on problem for nonlocal parabolic equations, where we are interested to recover the leading coefficient of nonlocal parabolic operators. The main contribution is that we can relate both…
In this article we prove quantitative unique continuation results for wave operators of the form $\partial$ 2 t -- div(c(x)$\nabla$$\bullet$) where the scalar coefficient c is discontinuous across an interface of codimension one in a…
We investigate the effect of small diffusion on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors of the principal eigenvalues, as…
For the heat equation in a bounded domain we give a stability result for a smooth diffusion coefficient. The key ingredients are a global Carleman-type estimate, a Poincar\'e-type estimate and an energy estimate with a single observation…
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
This work is devoted to the strong unique continuation problem for second order parabolic equations with nonsmooth coefficients. Introduction and bibliography have been revised.
In this paper, we investigate generalized Carleman kinetic equation for n$\ge$2 and prove convergence towards the solution of equation with fast diffusion or porous medium type, $u_t=\Delta u^m$ ($0\le m\le2$), in its diffusive hydrodynamic…
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…
We give an application of interpolation with a function parameter to parabolic differential operators. We introduce the refined anisotropic Sobolev scale that consists of some Hilbert function spaces of generalized smoothness. The latter is…
In this paper, we obtain new Carleman estimates for a class of variable coefficient degenerate elliptic operators whose constant coefficient model at one point is the so called Baouendi-Grushin operator. This generalizes the results…
In this work, we prove a Carleman estimate for a parabolic problem which has a dissipative degenerate term. The prove relies on choose a suitable weight function that change of sign inside the control domain.