Related papers: Age-dependent equations with non-linear diffusion
Ageing phenomena are observed in a large variety of dynamical systems exhibiting a slow relaxation from a non-equilibrium initial state. Ageing can be characterised in terms of the linear response R(t,s) at time t to a local perturbation at…
We investigate numerically the dynamics of three different spin models in the aging regime. Each of these models is meant to be representative of a distinct class of aging behavior: coarsening systems, discontinuous spin glasses, and…
This article investigates an energy balance model coupled to the primitive equations by a dynamic boundary condition with and without noise on the boundary. It is shown that this system is globally strongly well-posed both in the…
We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…
We consider a one-dimensional free boundary problem governed by a nonlinear diffusion - convection equation with a Neumann condition at fixed face $x=0$, which is variable in time and a like Stefan convective condition on the free boundary.…
The equation of state for a liquid in equilibrium, written in the potential energy landscape formalism, is generalized to describe out-of-equilibrium conditions. The hypothesis that during aging the system explores basins associated to…
We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of…
We investigate the relation between an applied potential and the corresponding stationary state occupation for nonequilibrium and overdamped diffusion processes. This relation typically becomes long ranged resulting in global changes for…
In this work, we introduce a cross-diffusion model that couples population density and occupied area to investigate how internal pressure drives growth and motility. By blending nonlinear nonlocal interactions with porous-medium diffusion…
For many applications of agent-based models (ABMs), an agent's age influences important decisions (e.g. their contribution to/withdrawal from pension funds, their level of risk aversion in decision-making, etc.) and outcomes in their life…
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…
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 linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations…
The chronological age used in demography describes the linear evolution of the life of a living being. The chronological age cannot give precise information about the exact developmental stage or aging processes an organism has reached. On…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications.…
A linear growth-diffusion equation is studied in a time-dependent interval whose location and length both vary. We prove conditions on the boundary motion for which the solution can be found in exact form, and derive the explicit expression…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…