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The conditions for the existence, uniqueness and boundedness of global solutions, as well as ultimate boundedness of solutions, and the conditions for the blow-up of solutions of nonregular semilinear differential-algebraic equations are…
Non-equilibrium steady states are subject to intense investigations but still poorly understood. For instance, the derivation of Fourier law in Hamiltonian systems is a problem that still poses several obstacles. In order to investigate…
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the influence of knowledge in the evolution of wealth in a system of agents which interact through the binary trades introduced in Cordier, Pareschi,…
This paper examines impulsive non-autonomous systems with grazing periodic solutions. Surfaces of discontinuity and impact functions of the systems are not depending on the time variable. That is, we can say that the impact conditions are…
We study a class of nonlinear kinetic Fokker-Planck type equations modeling quantum particles which obey the Bose-Einstein and Fermi-Dirac statistics, respectively. We establish the existence of classical solutions in the perturbative…
We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modelling of taxation and redistribution in a closed (trading market) society. This framework allows to describe the evolution…
The statistical-physical study of granular matter is essential to understand, from a fundamental point of view, the many different phenomena emerging in these classical many-body systems. Under rapid-flow conditions, granular materials…
We present a novel approach to kinetic theory modeling enabling the simulation of a generic, real gas presented by its corresponding equation of state. The model is based on mass, momentum and energy conservation, and unlike the lattice…
We consider two models for a two component gas mixture with translational and internal energy degrees of freedom described by a BGK approximation assuming that the number of particles of each species remains constant. The two species are…
A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but…
Many natural ecosystems harbor large numbers of coexisting species competing for far fewer distinct resources, in apparent defiance of the competitive exclusion principle. Various mechanisms have been proposed to explain this apparent…
We study evolution equations on networks that can be modeled by means of hyperbolic systems. We extend our previous findings in \cite{KraMugNic20} by discussing well-posedness under rather general transmission conditions that might be…
In view of some persistent recent reports on a singular kind of growth of the world wealth inequality, where a finite (often handful) number of people tend to possess more than the wealth of the planet's 50\% population, we explore here if…
We introduce a closure model for coarse-grained kinetic theories of polar active fluids. Based on a quasi-equilibrium approximation of the particle distribution function, the model closely captures important analytical properties of the…
A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean-field…
Difference Kinetic Equations are derived quantum mechanically in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors…
We consider the Boltzmann equation with external fields in strictly convex domains with the specular reflection boundary condition. We construct classical $C^1$ solutions away from the grazing set under the assumption that the external…
Individual constituent balance equations are often used to derive expressions for species-specific segregation velocities in flows of dense granular mixtures. We propose a semiempirical expression for the interspecies momentum exchange in…
We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…
We prove that linear collisional kinetic equations in the whole space without confinement mechanism display a long-time self-similar behaviour. This drastically improves the recently known results (decay estimates) about the solutions in…