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A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
Ignoring the differences between countries, human reproductive and dispersal behaviors can be described by some standardized models, so whether there is a universal law of population growth hidden in the abundant and unstructured data from…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
In this paper the spatial-temporal dynamics of the members of interacting populations is described by nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Here we tackle the problem of determining the distribution of the population density of a social space…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
In this paper we propose a macro-dynamic age-structured set-up for the analysis of epidemics/economic dynamics in continuous time. The resulting optimal control problem is reformulated in an infinite dimensional Hilbert space framework…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
A cross-diffusion system with Lotka-Volterra reaction terms in a bounded domain with no-flux boundary conditions is analyzed. The system is a nonlocal regularization of a generalized Busenberg-Travis model, which describes segregating…
In this article we have successfully obtained an exact solution of a particular case of SIR and SIS epidemic models given by Kermack and Mckendrick [1] for constant population, which are described by coupled nonlinear differential…
We determine the large-time behavior of unbounded solutions for the so-called viscous Hamilton Jacobi equation, $u_t - \Delta u + |Du|^m = f(x)$, in the quadratic and subquadratic cases (i.e., for $1<m\leq 2$), with a particular focus on…
In this work we suggest a simple mathematical model for the dynamics of the population of children and adolescents without problematic behavior (criminal activities etc.). This model represents a typical population growth equation but with…
A set of many identical interacting agents obeying a global additive constraint is considered. Under the hypothesis of equiprobability in the high-dimensional volume delimited in phase space by the constraint, the statistical behavior of a…
Infinite Leslie matrices, introduced by Demetrius forty years ago are mathematical models of age-structured populations defined by a countable infinite number of age classes. This article is concerned with determining solutions of the…
In recent years it has been increasing evidence that lognormal distributions are widespread in physical and biological sciences, as well as in various phenomena of economics and social sciences. In social sciences, the appearance of…
We generalize the classical knapsack and subset sum problems to arbitrary groups and study the computational complexity of these new problems. We show that these problems, as well as the bounded submonoid membership problem, are P-time…
We establish the global existence of weak solutions to a nonlinear kinetic Fokker--Planck equation with degenerate diffusion, under either inflow or partial absorption-reflection boundary conditions. The novelty of our approach lies in…