In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, here we show that the ill-posedness decreases when we increase the wave number.

This paper is concerned with the global well-posedness and inviscid limits of several systems of Boussinesq equations with fractional dissipation. Three main results are proven. The first result assesses the global regularity of two systems of equations close to the critical 2D Boussinesq equations. This is achieved by examining their inviscid limits. The second result relates the global regula...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

In this article, a new multidirectional monotone hybrid iteration algorithm for finding a solution to the split common fixed point problem is presented for two countable families of quasi-nonexpansive mappings in Banach spaces. Strong convergence theorems are proved. The application of the result is to consider the split common null point problem of maximal monotone operators in Banach spaces. ...

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...

The paper is concerned with properties of an ill-posed problem for the Helmholtz equation when Dirichlet and Neumann conditions are given only on a part Γ of the boundary ∂Ω. We present an equivalent formulation of this problem in terms of a moment problem defined on the part of the boundary where no boundary conditions are imposed. Using a weak definition of the normal derivative, we prove the...

We present new theoretical results which have implications in answering one of the fundamental questions in computer vision: recognition of surfaces and surface shapes. We state the conditions under which: (i) a surface can be recovered, uniquely, from the tangent plane map, in particular from the Gauss map; (ii) a surface shape can be recovered from the metric and the deforming forces. In case...

We show that the Benjamin-Ono equation is globally well-posed in H s (R) for s ≥ 1. This is despite the presence of the derivative in the non-linearity, which causes the solution map to not be uniformly continuous in H s for any s [15]. The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.

We consider the defocusing, ˙ H 1-critical Hartree equation for the radial data in all dimensions (n ≥ 5). We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term − I |x|≤A|I| 1/2 |u| 2 ∆ 1 |x| dxdt in the localized Morawetz identity to rule out the possibility of energy concentration, instead of ...