Study of a generalized logistic equation with nonlocal reaction term

A Logistic Equation with Refuge and Nonlocal Diffusion

In this work we consider the nonlocal stationary nonlinear problem (J ∗ u)(x) − u(x) = −λu(x) + a(x)u(x) in a domain Ω, with the Dirichlet boundary condition u = 0 in R \ Ω and p > 1. The kernel J involved in the convolution (J ∗ u)(x) = RN J(x− y)u(y) dy is a smooth, compactly supported nonnegative function with unit integral, while the weight a(x) is assumed to be nonnegative and is allowed t...

Universal Bounds for Global Solutions of a Diffusion Equation with a Mixed Local-nonlocal Reaction Term

In this paper we prove the existence of a universal, i.e. independent of the initial data, bound for global positive solutions of a diffusion equation with a mixed local-nonlocal reaction term. Such results are already known in some cases of local or nonlocal reaction terms.

Asymptotic Behavior of a Nonlocal Diffusive Logistic Equation

The long time behavior of a logistic-type equation modeling the motion of cells is investigated. The equation we consider takes into account birth and death processes using a simple logistic effect as well as a nonlocal motion of cells using a nonlocal Darcy's law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some inform...

On Oscillation of a Generalized Logistic Equation with Several Delays

Blowup Analysis for a Nonlocal Reaction Diffusion Equation with Potential

In this paper we investigate a nonlocal reaction diffusion equation with potential, under Neumann boundary. We obtain the complete classification of the parameters for which the solution blows up in finite time or exists globally. Moreover, we study the blowup rate and the blowup set for the blowup solution. Key–Words: Nonlocal diffusion, Blow up, Blowup rate, Blowup set