Related papers: Unique continuation property with partial informat…
In this article we deal with different forms of the unique continuation property for second order elliptic equations with nonlinear potentials of sublinear growth. Under suitable regularity assumptions, we prove the weak and the strong…
In this paper, we give the strong unique continuation property for a general two dimensional anisotropic elliptic system with real coefficients in a Gevrey class under the assumption that the principal symbol of the system has simple…
In this paper, we study the persistence properties and unique continuation for a dispersionless two-component system with peakon and weak kink solutions. These properties guarantee strong solutions of the two-component system decay at…
We present a simple and self-contained approach to establish the unique continuation property for some classical evolution equations of second order in a cylindrical domain. We namely discuss this property for wave, parabolic and…
This paper concerns about the weak unique continuation property of solutions of a general system of differential equation/inequality with a second order strongly elliptic system as its leading part. We put not only some natural assumption…
This paper is dedicated to the unique continuation properties of the solutions to nonlinear variational problems. Our analysis covers the case of nonlinear autonomous functionals depending on the gradient, as well as more general double…
We establish a unique continuation property for solutions of the differential inequality $|\nabla u|\leq V|u|$, where $V$ is locally $L^n$ integrable on a domain in $\mathbb R^n$. A stronger uniqueness result is obtained if in addition the…
We consider a unique continuation problem for the wave equation given data in a volumetric subset of the space time domain. In the absence of data on the lateral boundary of the space-time cylinder we prove that the solution can be…
We study a simplified nonlinear thermoelasticity model on two- and three-dimensional tori. A novel functional involving the Fisher information associated with temperature is introduced, extending the previous one-dimensional approach from…
The purpose of the current paper is twofold: to some extent it is intended as a review of the recent optimal result in [4] concerning the unique continuation property of solutions to the two-dimensional Zakharov-Kuznetsov equation. On the…
In this paper, we consider a nonlinear Fuchsian type partial differential equation of the second order in the complex domain. Under a very weak assumption, we show the uniqueness of the solution. The result is applied to the problem of…
This paper establishes a fundamental and surprising phenomenon in the theory of stochastic wave equations: the restoration of the unique continuation property (UCP) across characteristic hypersurfaces, a property that is known to fail…
We study the recovery of piecewise analytic density and stiffness tensor of a three-dimensional domain from the local dynamical Dirichlet-to-Neumann map. We give global uniqueness results if the medium is transversely isotropic with known…
Systems of the first order partial differential equations with singular solutions appear in many multiphysics problems and the weak formulation of solutions involve in many cases product of distributions. In this paper we study such a…
We establish a strong unique continuation property for stochastic parabolic equations. Our method is based on a suitable stochastic version of Carleman estimate. As far as we know, this is the first result for strong unique continuation…
These notes are intended as an introduction to the question of unique continuation for the wave operator, and some of its applications. The general question is whether a solution to a wave equation in a domain, vanishing on a subdomain has…
We consider solutions to the hyperbolic system of equations of ideal granular hydrodynamics with conserved mass, total energy and finite momentum of inertia and prove that these solutions generically lose the initial smoothness within a…
A time domain system of equations is proposed to model elastic wave propagation in an unbounded two-dimensional anisotropic solid using perfectly matched layer (PML). Starting from a system of first-order frequency domain stress-velocity…
For a genuinely nonlinear $2\times 2$ hyperbolic system of conservation laws, assuming that the initial data have small ${\bf L}^\infty$ norm but possibly unbounded total variation, the existence of global solutions was proved in a…
This paper is devoted to a study of the unique continuation property for stochastic parabolic equations. Due to the adapted nature of solutions in the stochastic situation, classical approaches to treat the the unique continuation problem…