Related papers: Analysis of a fractional cross-diffusion system fo…
In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels $\phi(x):=|x|^{-(n+\alpha)}$ for $\alpha\in(0,2)$. Here, we consider the critical case…
New estimates and global existence results are provided for a class of systems of cross diffusion equations arising from the modeling of chemotaxis with local sensing, possibly featuring a growth term of logistic-type as well. For sublinear…
The global-in-time existence of bounded weak solutions to the Maxwell-Stefan-Fourier equations in Fick-Onsager form is proved. The model consists of the mass balance equations for the partial mass densities and and the energy balance…
We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method with quantitative bounds. We show an algebraic $L^1$-convergence result using moderately interacting…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian and show…
We present a quantitative model for the biological evolution of species body masses within large groups of related species, e.g., terrestrial mammals, in which body mass M evolves according to branching (speciation), multiplicative…
We consider two evolution equations involving space fractional Laplace operator of order $0<s<1$. We first establish some existence and uniqueness results for the considered evolution equations. Next, we give some comparison theorems and…
The weak coupling limit for a quantum system, with discrete energy spectrum, coupled to a Bose reservoir with the most general linear interaction is considered: under this limit we have a quantum noise processes substituting for the field.…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
We study an initial boundary value problem for a cross-diffusion system in population dynamics. The mathematical challenge is due to the fact that the determinant of the coefficient matrix of the system changes signs. As a result, the…
The global-in-time existence and uniqueness of bounded weak solutions to a spinorial matrix drift-diffusion model for semiconductors is proved. Developing the electron density matrix in the Pauli basis, the coefficients (charge density and…
We prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are based on a maximal velocity bound, which states that the…
An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…
Population cross-diffusion systems of Shigesada-Kawasaki-Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion…
An implicit Euler finite-volume scheme for a degenerate cross-diffusion system describing the ion transport through biological membranes is analyzed. The strongly coupled equations for the ion concentrations include drift terms involving…
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…
This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier-Stokes…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…