In this paper we analyze the global existence of classical solutions to the initial boundary-
value problem for a nonlinear parabolic equation describing the collective behavior of an …

Mathematical models based on partial differential equations (PDEs) have become an
integral part of quantitative analysis in most branches of science and engineering, recently …

We discuss global existence and asymptotic behaviour of a price formation free boundary
model introduced by Lasry and Lions in 2007. Our results are based on a construction which …

In this paper we study the asymptotic behavior of a Boltzmann type price formation model,
which describes the trading dynamics in a financial market. In many of these markets trading …

Abstract Models of market microstructure at the order book scale can be split into two
families: First, the agent-based models [5] aiming at simulating a large number of agents …

Nous discutons l'existence locale et globale, ainsi que l'unicité des solutions pour le modèle
de formation des prix à frontière libre avec des conditions aux bords de Neumann …

We consider the problem of estimating the density of buyers and vendors in a nonlinear
parabolic price formation model using measurements of the price and the transaction rate …

We study the existence and asymptotics for large time of the solutions to a one dimensional
evolution equation with non-standard right-hand side. The right-hand side involves the …

In this paper we consider a free boundary problem for the p-Laplace operator which can be
seen as a discrete version of the so-called Bernoulli free boundary problem. In this …

A well-known model due to J.-M. Lasry and PL Lions that presents the evolution of prices in
a market as the evolution of a free boundary in a diffusion equation is modified in order to …