Related papers: Inverse Problems for Hyperbolic Equations

We study the quasi-static limit for the $L^\infty$ entropy weak solution of scalar one-dimensional hyperbolic equations with strictly concave or convex flux and time dependent boundary conditions. The quasi-stationary profile evolves with…

Here a mixed problem for a nonlinear hyperbolic equation with Neumann boundary value condition is investigated, and a priori estimations for the possible solutions of the considered problem are obtained. These results demonstrate that any…

This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the…

The stability theory for hyperbolic initial boundary value problems relies most of the time on the Laplace transform with respect to the time variable. For technical reasons, this usually restricts the validity of stability estimates to the…

We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…

In this paper, a time domain enclosure method for an inverse obstacle scattering problem of electromagnetic wave is introduced. The wave as a solution of Maxwell's equations is generated by an applied volumetric current having an {\it…

We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\mathbb{R}^n$. A reformulation leads to a a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial…

We consider a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. We discuss on the inverse problem of determining the shape of the interface from Dirichlet and Neumann data at one…

We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal operators with bounded measurable coefficients. Moreover, we…

We prove various new trigonometric and hyperbolic inequalities of Jordan, Wilker, Huygens or Cusa-Huygens type. Connections with bivariate means, as well as monotonicity and convexity properties are pointed out, too.

We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time…

In this paper, we study the backward problem of determining initial condition for some class of nonlinear parabolic equations in multidimensional domain where data are given under random noise. This problem is ill-posed, i.e., the solution…

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…

In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent leading coefficient for positive operators. First, we consider the direct problem, and the unique existence of the…

We give necessary and sufficient conditions for the existence of weak solutions of a parabolic problem corresponding to the Kolmogorov operators perturbed by a multipolar inverse square potential with respect to the Gaussian probability…

We obtain bounds on hyperbolic volume for periodic links and Conway sums of alternating tangles. For links that are Conway sums we also bound the hyperbolic volume in terms of the coefficients of the Jones polynomial.

Consider the planar restricted $(N+1)$-body problem with trajectories of the $N(\ge 2)$ primaries forming a collision-free periodic solution of the $N$-body problem, for any positive energy $h$ and directions $\theta_{\pm} \in [0, 2\pi)$,…

We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…

Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…

A hyperbolic problem wich combines a classical(Dirichlet) and a non-local contraint is considered.The existence and uniqueness of strong solutions are proved,we use a functionnal analysis method based on a priori estimate and on the density…