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pro vyhledávání: '"KLIBANOV, MICHAEL V."'
A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called "Mean Field Games System" (MFGS), which is derived in the mean field games (MFG) theory. Thi
Externí odkaz:
http://arxiv.org/abs/2405.10479
Autor:
Klibanov, Michael V.
The time dependent experimental data are always collected at discrete grids with respect to the time t. The step size h of such a grid is always separated from zero by a certain positive number. The same is true for all computations, which are always
Externí odkaz:
http://arxiv.org/abs/2404.16246
Let S,I and R be susceptible, infected and recovered populations in a city affected by an epidemic. The SIR model of Lee, Liu, Tembine, Li and Osher, \emph{SIAM J. Appl. Math.},~81, 190--207, 2021 of the spatiotemoral spread of epidemics is considere
Externí odkaz:
http://arxiv.org/abs/2401.02070
H\"older stability estimate and uniqueness are proven for a retrospective problem of Mean Field Games with a non-quadratic Hamiltonian. The previous result was only for the quadratic Hamiltonian. The main tool is the apparatus of Carleman estimates.
Externí odkaz:
http://arxiv.org/abs/2310.18799
The globally convergent convexification numerical method is constructed for a Coefficient Inverse Problem for the Mean Field Games System. A coefficient characterizing the global interaction term is recovered from the single measurement data. In part
Externí odkaz:
http://arxiv.org/abs/2310.08878
The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game of infinite
Externí odkaz:
http://arxiv.org/abs/2306.14404
Autor:
Klibanov, Michael V.
A Coefficient Inverse Problem (CIP) of the determination of a coefficient of the Mean Field Games System (MFGS) of the second order is considered. The input data are generated by a single measurement event. Lateral Cauchy data, i.e. Dirichlet and Neu
Externí odkaz:
http://arxiv.org/abs/2306.03349
The mean field games (MFG) theory has broad application in mathematical modeling of social phenomena. The Mean Field Games System (MFGS) is the key to the MFG theory. This is a system of two nonlinear parabolic partial differential equations with two
Externí odkaz:
http://arxiv.org/abs/2305.01065
Our objective is to calculate the derivatives of data corrupted by noise. This is a challenging task as even small amounts of noise can result in significant errors in the computation. This is mainly due to the randomness of the noise, which can resu
Externí odkaz:
http://arxiv.org/abs/2304.05909