@article{57560db0657941a5bb59b43a9622262b,
title = "ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION",
abstract = "We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results. {\textcopyright} 2009 World Scientific Publishing Company.",
author = "MARKOWICH, {P. A.} and N. MATEVOSYAN and J.-F. PIETSCHMANN and M.-T. WOLFRAM",
note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: This publication is based on work supported by Award No. KUK-I1-007-43 of Peter Markowich, made by King Abdullah University of Science and Technology (KAUST) and by the Leverhulme Trust through the Research Grant entitled {"}KINETIC AND MEAN FIELD PARTIAL DIFFERENTIAL MODELS FOR SOCIO-ECONOMIC PROCESSES{"} (PI Peter Markowich). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",
year = "2011",
month = nov,
day = "21",
doi = "10.1142/S0218202509003978",
language = "English (US)",
volume = "19",
pages = "1929--1957",
journal = "Mathematical Models and Methods in Applied Sciences",
issn = "0218-2025",
publisher = "World Scientific Publishing",
number = "10",
}