Strong Solution for Fractional Mean Field Games with Non-Separable Hamiltonians
نویسندگان
چکیده
In this paper, we establish the existence and uniqueness of a strong solution to fractional mean field games system with non-separable Hamiltonians, where exponent σ∈(12,1). Our result is new for which generalizes work D.M. Ambrose integral case. The important step choose appropriate order function spaces use Banach fixed-point theorem under stronger assumptions Hamiltonians.
منابع مشابه
Strong Solutions for Time-dependent Mean Field Games with Non-separable Hamiltonians
We prove existence theorems for strong solutions of time-dependent mean field games with non-separable Hamiltonian. In a recent announcement, we showed existence of small, strong solutions for mean field games with local coupling. We first generalize that prior work to allow for non-separable Hamiltonians. This proof is inspired by the work of Duchon and Robert on the existence of small-data vo...
متن کاملSimple strong glass forming models: mean-field solution with activation
We introduce simple models, inspired by previous models for froths and covalent glasses, with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems. These models are also a generalization of backgammon or urn models to a non-constant number of particles, where entropic barriers are replaced by energy barriers, allowing for the existence of activat...
متن کاملMean-Field Games for Marriage
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple...
متن کاملSmall Strong Solutions for Time-dependent Mean Field Games with Local Coupling
For mean field games with local coupling, existence results are typically for weak solutions rather than strong solutions. We identify conditions on the Hamiltonian and the coupling which allow us to prove the existence of small, locally unique, strong solutions over any finite time interval in the case of local coupling; these conditions place us in the case of superquadratic Hamiltonians. For...
متن کاملMean Field Games
We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field approach to modelling in Economics and Finance (or other related subjects. . . ). Roughly speaking, we are concerned with situations that involve a very large number of “rational players” with a limited inform...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fractal and fractional
سال: 2022
ISSN: ['2504-3110']
DOI: https://doi.org/10.3390/fractalfract6070362