Journal
APPLIED MATHEMATICS AND OPTIMIZATION
Volume 59, Issue 2, Pages 233-246Publisher
SPRINGER
DOI: 10.1007/s00245-008-9052-y
Keywords
Mean field model; Diffusion equation; Dynamical equilibrium in price formation; Asymptotic decay
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Funding
- NSF [DMS-0807636]
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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 derivative of the solution computed at a given point. Existence is proven through a fixed point argument. When the problem is considered in a bounded interval, it is shown that the solution decays exponentially to the stationary state. This problem is a particular case of a mean-field free boundary model proposed by Lasry and Lions on price formation and dynamic equilibria.
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