Asymptotic Behavior of a Nonlocal Diffusive Logistic Equation

A Nonlocal Convection-diffusion Equation

In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut = J ∗u−u+G ∗ (f(u))− f(u) in R, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equatio...

Quenching Time for a Nonlocal Diffusion Problem with Large Initial Data

Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation

In this paper, we consider a dynamical model of population biology which is of the classical Fisher type, but the competition interaction between individuals is nonlocal. The existence, uniqueness, and stability of the steady state solution of the nonlocal problem on a bounded interval with homogeneous Dirichlet boundary conditions are studied. Mathematics subject classification (2010). 35K57 ·...

Implicit Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime

We design several implicit asymptotic-preserving schemes for the linear semiconductor Boltzmann equation with a diffusive scaling, which lead asymptotically to the implicit discretizations of the drift-diffusion equation. The constructions are based on a stiff relaxation step and a stiff convection step obtained by splitting the system equal to the model equation. The one space dimensional sche...

Nonlocal Analysis of Longitudinal Dynamic Behavior of Nanobars with Surface Energy Effect

Due to considerable stored energy in surfaces of nano-scales in comparison with the stored energy in their bulk, considering the surface energy is necessary for the analysis of various behaviors of nano-scales for more precise design and manufacturing. In this article, the longitudinal dynamic behavior of nanobars in the presence of the surface energy parameters is studied. To this end, the lon...