Related papers: A new approach to hyperbolic inverse problems II (…
In this work we present an adaptive boundary element method for computing the electromagnetic response of wave interactions in hyperbolic metamaterials. One unique feature of hyperbolic metamaterial is the strongly directional wave in its…
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 establish Lipschitz stability for both the potential and the initial conditions from a single boundary measurement in the context of a hyperbolic boundary initial value problem. In our setting, the initial conditions are allowed to…
In this paper we study the finite element approximation of systems of second-order nonlinear hyperbolic equations. The proposed numerical method combines a $hp$-version discontinuous Galerkin finite element approximation in the time…
In this paper we provide a criterion for global secondary bifurcation via symmetry breaking. As an application, the occurrence of period-doubling bifurcations for the Lugiato-Lefever equation is proved.
In this study, we present a simulation-based numerical method for solving a class of singularly perturbed second-order differential equations that come from a simplified biologically motivated model of human gait. Important physical factors…
The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving existence and…
Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…
In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…
We formulate the immersed-boundary method (IBM) as an inverse problem. A control variable is introduced on the boundary of a larger domain that encompasses the target domain. The optimal control is the one that minimizes the mismatch…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
The Cauchy slicings for globally hyperbolic spacetimes and their relation with the causal boundary are surveyed and revisited, starting at the seminal conformal boundary constructions by R. Penrose. Our study covers: (1) adaptive…
In this article we introduce a hyperbolic metric on the (normalized) space of stability conditions on projective K3 surfaces $X$ with Picard rank $\rho (X) =1$. And we show that all walls are geodesic in the normalized space with respect to…
In this work, we study the inverse problem of analog gravity systems which admit rotation and energy-dependent boundary conditions. By extending two recent results, we provide a recipe that allows one to relate resonant transmission spectra…
The initial data in the polygon approach to (2+1)D gravity coupled to point particles are constrained by the vertex equations and the particle equations. We establish the hyperbolic nature of the vertex equations and derive some…
We show that a complete Riemannian manifold, as well as time independent smooth lower order terms appearing in a first order symmetric perturbation of a Riemannian wave operator can be uniquely recovered, up to the natural obstructions,…
Gradient descent generalises naturally to Riemannian manifolds, and to hyperbolic $n$-space, in particular. Namely, having calculated the gradient at the point on the manifold representing the model parameters, the updated point is obtained…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…
We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…