Related papers: Inverse problems in the multidimensional hyperboli…
In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary…
We present a new derivation of the equations governing the oscillations of slowly rotating relativistic stars. Previous investigations have been mostly carried out in the Regge-Wheeler gauge. However, in this gauge the process of…
This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…
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,…
The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces…
We consider an inverse problem associated with $n$-dimensional asymptotically hyperbolic orbifolds $(n \geq 2)$ having a finite number of cusps and regular ends. By observing solutions of the Helmholtz equation at the cusp, we introduce a…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…
In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results,…
This paper deals with left invertibility problem of implicit hyperbolic systems with delays in infinite dimensional Hilbert spaces. From a decomposition procedure, invertibility for this class of systems is shown to be equivalent to the…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
Time evolution of quantum systems is accelerated by the fast-forward scaling. We reformulate the method to study systems in a finite-dimensional Hilbert space. For several simple systems, we explicitly construct the acceleration potential.…
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
Inverse problems are central to a wide range of fields, including healthcare, climate science, and agriculture. They involve the estimation of inputs, typically via iterative optimization, to some known forward model so that it produces a…
Motivated by a new kind of initial boundary value problem (IBVP) with a free boundary arising in wave-structure interaction, we propose here a general approach to one-dimensional IBVP as well as transmission problems. For general strictly…
The possibility of physics in multiple time dimensions is investigated. Drawing on recent work by Walter Craig and myself, I show that, contrary to conventional wisdom, there is a well-posed initial value problem--deterministic, stable…
The paper examines the existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations. Namely, sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those…
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
We consider the generalized spectral estimation problem in infinite dimensional spaces. We solve this problem using the boundary control approach to inverse theory and provide an application to the initial boundary value problem for a…