Related papers: Singular limits for models of selection and mutati…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
The existence of global weak solutions to the cross-diffusion model of Shigesada, Kawasaki, and Teramoto for an arbitrary number of species is proved. The model consists of strongly coupled parabolic equations for the population densities…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
We consider nonlinear nonlocal diffusive evolution equations, governed by fractional Laplace-type operators, fractional time derivative and involving porous medium type nonlinearities. Existence and uniqueness of weak solutions are…
Interacting systems consisting of two rotators and a point mass near a hyperbolic fixed point are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of quasi periodic…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
We re-analyze the quasi-linear self consistent dynamics for the beam-plasma instability, by comparing the theory predictions to numerical simulations of the corresponding Hamiltonian system. While the diffusive features of the asymptotic…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…
We study a time-fractional Fisher-KPP equation involving a Riemann-Liouville fractional derivative acting on the diffusion term, as derived by Angstmann and Henry (Entropy, 22:1035, 2020). The model captures memory effects in diffusive…
The behaviour is investigated of solutions to a diffusion equation on the real line with nonlocal and singular reaction term, i.e., given by a Dirac source or sink at the origin. It gives a simplified representation of for example a control…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact…
We provide a mathematical analysis of appearance of the concentrations (as Dirac masses) of the solution to a Fokker-Planck system with asymmetric potentials. This problem has been proposed as a model to describe motor proteins moving along…
In this note we provide some precise estimates explaining the diffusive structure of partially dissipative systems with time-dependent coefficients satisfying a uniform Kalman rank condition. Precisely, we show that under certain (natural)…
The existence of global nonnegative martingale solutions to cross-diffusion systems of Shigesada-Kawasaki-Teramoto type with multiplicative noise is proven. The model describes the stochastic segregation dynamics of an arbitrary number of…
We study the asymptotic behaviour of stationary densities of one-dimensional random diffeomorphisms, at the boundaries of their support, which correspond to deterministic fixed points of extremal diffeomorphisms. In particular, we show how…
We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac's approach, the nonlinear model is approximated by a mean field linear evolution…
We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…
We study a fractional cross-diffusion system that describes the evolution of multi-species populations in the regime of large-distance interactions in a bounded domain. We prove existence and weak-strong uniqueness results for the…