Determining state space anomalies in mean field games

Nonlinearity, Journal Year: 2025, Volume and Issue: 38(2), P. 025010 - 025010

Published: Jan. 17, 2025

Abstract In this paper, we are concerned with the inverse problem of determining anomalies in state space associated stationary mean field game (MFG) system. We establish novel unique identifiability results for intrinsic structure these MFGs systems, including their topological and parameter configurations, several general scenarios practical interest, traffic flow, market economics epidemics. To best our knowledge, is first work that considers nonlinear coupled MFG

Language: Английский

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Determining a Stationary Mean Field Game System from Full/Partial Boundary Measurement

SIAM Journal on Mathematical Analysis, Journal Year: 2025, Volume and Issue: 57(1), P. 661 - 681

Published: Jan. 16, 2025

.In this paper, we propose and study the utilization of Dirichlet-to-Neumann map to uniquely identify discount functions \(r, k\) cost function \(F\) in a stationary mean field game (MFG) system. This features several technical novelties that make it highly intriguing challenging. First, involves coupling two nonlinear elliptic partial differential equations. Second, simultaneous recovery multiple parameters poses significant implementation challenge. Third, there is probability measure constraint coupled equations consider. Finally, limited information available from boundary measurements adds another layer complexity problem. Considering these challenges problems, present an enhanced higher-order linearization method tackle inverse problem related MFG Our proposed approach linearizing around pair zero solutions fulfilling measurement by adjusting positive input at boundary. It worth emphasizing technique not only applicable for identifying using full-boundary but also effective utilizing partial-boundary measurements.Keywordsstationary gamesmultiple parametersunique identifiabilityfull/partial measurementCGO solutionsMSC codes49N8049N4591A16

Language: Английский

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On inverse problems in multi-population aggregation models

Journal of Differential Equations, Journal Year: 2024, Volume and Issue: 414, P. 94 - 124

Published: Sept. 10, 2024

Language: Английский

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Spatiotemporal monitoring of epidemics via solution of a coefficient inverse problem

Inverse Problems and Imaging, Journal Year: 2025, Volume and Issue: 0(0), P. 0 - 0

Published: Jan. 1, 2025

Language: Английский

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Dynamical analysis of a predator-prey system with fear-induced dispersal between patches

Mathematical Biosciences & Engineering, Journal Year: 2025, Volume and Issue: 22(5), P. 1159 - 1184

Published: Jan. 1, 2025

In this paper, a patchy model in which the migration is induced by fear effect on predator was investigated. By applying dynamical theory, complete study persistence of system and local/global stability equilibria were discussed. Choosing diffusion coefficient $ D_1 as bifurcation parameter, transcritical occurring near trivial equilibrium demonstrated. We concluded that low dispersal favorable for coexistence both species, but large leads to extinction species. There an optimal make density prey population reach its maximum. addition, level k maximum cost \eta are beneficial total prey.

Language: Английский

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Determining a parabolic system by boundary observation of its non-negative solutions with biological applications

Inverse Problems, Journal Year: 2023, Volume and Issue: 40(2), P. 025009 - 025009

Published: Dec. 12, 2023

Abstract In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation its non-negative solutions. physical setup, solutions represent certain probability densities in different contexts. We innovate successive linearisation method by further developing high-order variation scheme which can both ensure positivity and effectively tackle problem. This enables us to establish several novel unique identifiability results for rather general setup. For theoretical perspective, our study addresses an important topic partial differential equation (PDE) analysis on how characterise function spaces generated products non-positive PDEs. As typical practically interesting application, apply problems ecological population models, where positive signify densities.

Language: Английский

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Periodic measures for a neural field lattice model with state dependent superlinear noise

Electronic Research Archive, Journal Year: 2024, Volume and Issue: 32(6), P. 4011 - 4024

Published: Jan. 1, 2024

<abstract><p>The primary focus of this paper lies in exploring the limiting dynamics a neural field lattice model with state dependent superlinear noise. First, we established well-posedness solutions to these stochastic systems and subsequently proved existence periodic measures for system space square-summable sequences using Krylov-Bogolyubov's method. The cutoff techniques uniform estimates on tails was employed establish tightness family probability distributions system's solutions.</p></abstract>

Language: Английский

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Uniqueness principle for fractional (non)-coercive anisotropic polyharmonic operators and applications to inverse problems

Inverse Problems and Imaging, Journal Year: 2024, Volume and Issue: 0(0), P. 0 - 0

Published: Jan. 1, 2024

Language: Английский

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A frozen Levenberg-Marquardt-Kaczmarz method with convex penalty terms and two-point gradient strategy for ill-posed problems

Applied Numerical Mathematics, Journal Year: 2024, Volume and Issue: unknown

Published: Nov. 1, 2024

Language: Английский

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