4 papers
Semi-discrete multi-to -one dimensional variational problems
Omar Abdul Halim, Daniyar Omarov, Brendan Pass
We study a class of semi-discrete variational problems that arise in economic matching and game theory, where agents with continuous attributes are matched to a finite set of outco…
Multi-to -one dimensional and semi-discrete screening
Omar Abdul Halim, Brendan Pass
We study the monopolist's screening problem with a multi-dimensional distribution of consumers and a one-dimensional space of goods. We establish general conditions under which sol…
Asymptotic regimes of an integro-difference equation with discontinuous kernel
Omar Abdul Halim, Mohammad El Smaily
This paper is concerned with an integral equation that models discrete time dynamics of a population in a patchy landscape. The patches in the domain are reflected through the disc…
The optimal initial datum for a class of reaction-advection-diffusion equations
Omar Abdul Halim, Mohammad El Smaily
We consider a reaction-diffusion model with a drift term in a bounded domain. Given a time we prove the existence and uniqueness of an initial datum that maximizes the total m…