相关论文: Self-similarity in a General Aggregation-Fragmenta…
A spectral problem is considered in a thin $3D$ graph-like junction that consists of three thin curvilinear cylinders that are joined through a domain (node) of the diameter $\mathcal{O}(\varepsilon),$ where $\varepsilon$ is a small…
We consider a string with fixed endpoints where the mass density and/or the elastic coefficient vary in a self-affine way as function of position. It is demonstrated how the eigenvalues in the asymptotic limit are distributed. Scaling laws…
When wind blows over water, ripples are generated on the water surface. These ripples can be regarded as perturbations of the wind field, which is modelled as a parallel inviscid flow. For a given wavenumber $k$, the perturbed…
We determine the shape which minimizes, among domains with given measure, the first eigenvalue of the anisotropic laplacian perturbed by an integral of the unknown function. Using also some properties related to the associated \lq\lq…
We investigate the behavior of the dichotomy spectrum of nonautonomous linear systems under general growth rates. By introducing comparison criteria we clarify how $\mu$-dichotomy and $\mu$-bounded growth interact. We also study the…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…
The dynamic theory of inhomogeneous populations developed during the last decade predicts several essential new dynamic regimes applicable even to the well-known, simple population models. We show that, in an inhomogeneous population with a…
Morphoelasticity represents a foundational theory for tracing back growth, remodelling, and morphogenesis, yet crucial challenges persist. A unified growth law -- independent of a priori assumptions about constitutive relations or specified…
We consider a cell population described by an age-structured partial differential equation with time periodic coefficients. We assume that division only occurs after a minimal age (majority) and within certain time intervals. We study the…
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation…
We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of…
The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here we study the influence of finite-sized…
We study the mathematical properties of a model of cell division structured by two variables, the size and the size increment, in the case of a linear growth rate and a self-similar fragmentation kernel. We first show that one can construct…
We consider a one dimensional transport model with nonlocal velocity given by the Hilbert transform and develop a global well-posedness theory of probability measure solutions. Both the viscous and non-viscous cases are analyzed. Both in…
An explicit solution for a growth fragmentation equation with constant dislocation measure is obtained. In this example the necessary condition for the general results in \cite{BW} about the existence of global solutions in the so called…
We provide the exact large-time behavior of the tail distribution of the extinction time of a self-similar fragmentation process with a negative index of self-similarity, improving thus a previous result on the logarithmic asymptotic…
The second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane, limiting half-space, makes harmonious oscillations in the plane. The kinetic equation with modelling integral of collisions in the form…
In the present work the second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane limiting half-space makes harmonious fluctuations with variable amplitude in the plane. The amplitude changes on the…
We study planar graphs with large negative curvature outside of a finite set and the spectral theory of Schr{\"o}dinger operators on these graphs. We obtain estimates on the first and second order term of the eigenvalue asymptotics.…
We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of individuals to infinity we obtain a nonlinear transport…