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110 papers · 1 filter
A Survey on the Div-Curl Lemma and Some Extensions to Fractional Sobolev Spaces
Maicol Caponi
This survey is a chapter of a forthcoming book. This chapter recalls the classical formulation of the Div-Curl lemma along with its proof, and presents some possible generalization…
Time-delayed opinion dynamics with leader-follower interactions: consensus, stability, and mean-field limits
Young-Pil Choi, Chiara Cicolani, Cristina Pignotti
We study a time-delayed variant of the Hegselmann-Krause opinion formation model featuring a small group of leaders and a large group of non-leaders. In this model, leaders influen…
Existence and spectral stability analysis of viscous-dispersive shock profiles for isentropic compressible fluids of Korteweg type
R. Folino, C. Lattanzio, R. G. Plaza
The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is conside…
A priori error estimates for the -method for the flow of nonsmooth velocity fields
Gennaro Ciampa, Tommaso Cortopassi, Gianluca Crippa +2
Velocity fields with low regularity (below the Lipschitz threshold) naturally arise in many models from mathematical physics, such as the inhomogeneous incompressible Navier-Stokes…
On stability of one-dimensional Hughes' dynamics with affine costs
Boris Andreianov, Simone Fagioli, Massimiliano D. Rosini +1
We investigate stability issues for the one-dimensional variant of the celebrated Hughes model for pedestrian evacuation. The cost function is assumed to be affine, which is a sett…
Conservation Laws with Discontinuous Gradient-Dependent Flux: the Unstable Case
Debora Amadori, Alberto Bressan, Wen Shen
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions or , when th…