On a parabolic free boundary equation modeling price formation

Peter Markowich, N. Matevosyan, J. F. Pietschmann, Marie-Therese Wolfram

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1929-1957
Number of pages29
JournalMathematical Models and Methods in Applied Sciences
Issue number10
StatePublished - 2009
Externally publishedYes

Bibliographical 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.


  • Free boundary problem
  • Partial differential equations
  • Price formation

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation


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