期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 19, 期 10, 页码 1929-1957出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202509003978
关键词
Partial differential equations; free boundary problem; price formation
资金
- King Abdullah University of Science and Technology (KAUST) [KUK-I1-007-43]
- Leverhulme Trust
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.
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