Related papers: On global uniqueness for an IBVP for the time-harm…
We consider a regular and bounded dielectric body moving at a speed $|V|$, following a constant vector field $V$, with respect to a reference frame. In this frame, the special relativity implies that the Maxwell system is derived through…
In this paper, we investigate properties of unique continuation for hyperbolic Schr\"odinger equations with time-dependent complex-valued electric fields and time-independent real magnetic fields. We show that positive masses inside of a…
This work is concerned with establishing the existence and uniqueness of the solution to a mixed-type degenerate boundary value problem for a relativistic magnetohydrodynamics system. We first consider a full relativistic…
The magnetic field outside the earth is in good approximation a harmonic vector field determined by its values at the earth's surface. The direction problem seeks to determine harmonic vector fields vanishing at infinity and with prescribed…
We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order $\alpha \in (0,1)$ which are subject to non-zero Neumann boundary conditions. We prove the uniqueness for an inverse…
Motivated by diffusion processes on metric graphs and ramified spaces, we consider an abstract setting for interface problems with coupled dynamic boundary conditions belonging to a quite general class. Beside well-posedness, we discuss…
It is shown that every regular electromagnetic field in vacuum identically satisfy Maxwell equations in a new manifold where the roles of space and time have been exchanged. The new metric is Lorentzian, depends on the particular solution…
In this work we continue our study initiated in \cite{GFGP} on the uniqueness properties of real solutions to the IVP associated to the Benjamin-Ono (BO) equation. In particular, we shall show that the uniqueness results established in…
This paper considers the time-harmonic Maxwell equations with impedance boundary condition.We present $H^2$-norm bound and other high-order norm bounds for strong solutions. The $H^2$-estimate have been derived in [M. Dauge, M. Costabel and…
We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…
We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the…
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
When a (frequency-domain) boundary value problem involving a homogeneous linear material is solved to assess the validity of the Post constraint, a conflict arises between the fundamental differential equations of electromagnetism in the…
In the paper boundary-value problem for a multidimensional system of partial differential equations with fractional derivatives in Riemann-Liouville sense with constant coefficients is studied in a rectangular domain. The existence and…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
We consider a system of two singularly perturbed Boundary Value Problems (BVPs) of convection-diffusion type with discontinuous source terms and a small positive parameter multiplying the highest derivatives. Then their solutions exhibit…
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and…
We study different types of spacetime singularities which emerge in the context of disformal electrodynamics. The latter is characterized by transformations of the background metric which preserve regular (non-null) solutions of Maxwell…
In this paper, we study an inverse boundary value problem for the Jordan--Moore--Gibson--Thompson equation on a simple Riemannian manifold. We consider an all boundary measurement map that maps Dirichlet boundary data and initial data to…