Related papers: Feynman's inverse problem
We generalize the method used by M{\ae}hlen & Seth [17] used to prove the existence of small-amplitude asymmetric solutions to the capillary-gravity Whiham equation, so that it can be applied directly to a class of similar equations. The…
In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant differential equation capable to describe relativistic particle with mass and internal space-time structure. By making use of new variables that differentiate between…
This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…
We investigate the inverse problem of recovering an initial source for the wave equation with fractional attenuation, motivated by photoacoustic tomography (PAT). The attenuation is modeled by a Caputo fractional derivative of order…
A new derivation of the Bernoulli equation for water waves in three-dimensional rotating and translating coordinate systems is given. An alternative view on the Bateman-Luke variational principle is presented. The variational principle…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We consider the Cauchy problem for a second order quasi-linear partial differential equation with an admissible parabolic degeneration such that the given functions described the initial conditions are defined on a closed interval. We study…
We consider three-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension, where the upper fluid is bounded above by a rigid lid and the lower fluid is bounded below by a flat bottom. We…
This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of $\mathbb R^d$ or in the whole space $\mathbb R^d$. Based on a newly…
We consider a dynamic inverse problem for a dynamical system which describes the propagation of waves in a Krein string. The problem is reduced to an integral equation and an important special case is considered when the string density is…
In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…
In this work, we study the inverse problem of determining a potential coefficient in an abstract wave equation that includes a lower-order term. The equation incorporates a time-fractional derivative in the Caputo sense, as well as a…
This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the…
We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with…
We consider the inverse Calder\'on problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually…
The determination of Parton Distribution Functions from a finite set of data is a typical example of an inverse problem. Inverse problems are notoriously difficult to solve, in particular when a robust determination of the uncertainty in…
In geophysical environments, wave motions that are shaped by the action of gravity and global rotation bear the name of gravito-inertial waves. We present a geometrical description of gravito-inertial surface waves, which are low-frequency…
We study co--rotational wave maps from $(3+1)$--Minkowski space to the three--sphere $S^3$. It is known that there exists a countable family $\{f_n\}$ of self--similar solutions. We investigate their stability under linear perturbations by…
We discuss concepts and review results about the Cauchy problem for the Fornberg-Whitham equation, which has also been called Burgers-Poisson equation in the literature. Our focus is on a comparison of various strong and weak solution…