Related papers: Feynman's inverse problem
The inverse problem of reconstructing a source term from boundary measurements, for the wave equation, is revisited. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small…
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…
We solve the Cauchy problem of the Ward model in light-cone coordinates using the inverse spectral (scattering) method. In particular we show that the solution can be constructed by solving a $2\times 2$ local matrix Riemann-Hilbert problem…
We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…
We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
A version of the convexification globally convergent numerical method is constructed for a coefficient inverse problem for a wave-like partial differential equation. The presence of the Carleman Weight Function in the corresponding…
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…
This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…
We establish the inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data. In particular, it is employed to prove existence of weak solutions for the corresponding Cauchy problem.
When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is…
We present a link between the theory of deep water waves and that of bubble surface perturbations. Theory correspondence is shown analytically for small wavelengths in the linear regime and investigated numerically in the nonlinear regime.…
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…
In this paper we construct periodic capillarity-gravity water waves with a piecewise constant vorticity distribution. They describe water waves traveling on superposed linearly sheared currents that have different vorticities. This is…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…
We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted…
We establish global well-posedness and scattering for wave maps from $d$-dimensional hyperbolic space into Riemannian manifolds of bounded geometry for initial data that is small in the critical Sobolev space for $d \geq 4$. The main…
The paper investigates the sensitivity of the inverse problem of recovering the velocity field in a bounded domain from the boundary dynamic Dirichlet-to-Neumann map (DDtN) for the wave equation. Three main results are obtained: (1)…
The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…