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.
Original language | English (US) |
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Pages (from-to) | 1929-1957 |
Number of pages | 29 |
Journal | Mathematical Models and Methods in Applied Sciences |
Volume | 19 |
Issue number | 10 |
DOIs | |
State | Published - 2009 |
Externally published | Yes |
Keywords
- Free boundary problem
- Partial differential equations
- Price formation
ASJC Scopus subject areas
- Applied Mathematics
- Modeling and Simulation