We establish the existence and uniqueness of a solution to master equation for mean field game controls with absorption. The arises as continuum limit dynamic exhaustible resources modeling Cournot competition between producers. proof relies on an analysis forward-backward system nonlocal Hamilton-Jacobi/Fokker-Planck equations Dirichlet boundary conditions. In particular, we new priori estimat...

In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69–82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the ga...

Subwavelength electromagnetic field localization has been central to photonic research in the last decade, allowing us enhance sensing capabilities as well increase coupling between photons and material excitations. The strong ultrastrong light–matter regime terahertz range using split-ring resonators coupled magnetoplasmons widely investigated, achieving successive world records for largest ev...

The classical theory of electrokinetic phenomena is based on the mean-field approximation that the electric field acting on an individual ion is self-consistently determined by the local mean charge density. This paper considers situations, such as concentrated electrolytes, multivalent electrolytes, or solvent-free ionic liquids, where the mean-field approximation breaks down. A fourth-order m...

The nonlocal nonlinear buckling of a double layer graphene sheet (DLGS) covered by zinc oxide (ZnO) piezoelectric layers is investigated in this study. The surrounding circumstances of the system are considered as a Pasternak foundation including spring constants and a shear layer. Graphene sheets are subjected to longitudinal magnetic field and biaxial forces. On the other hand, the ZnO piezoe...

A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function which can be derived from the maximally nonlocal Lagrangian. The corresponding canonical equations are derived through the standard procedure in local theory and appear much like those local ones, though the implication of the equations is la...