منابع مشابه
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...
متن کاملErratum to: Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation
We show that the existence of a principal eigenvalue of a linear differential operator claimed in [4] does not always hold; hence, the proof of the stability and uniqueness of positive steady-state solution in [4] are not correct. For the linearized operator (φ ∈ X = {v ∈ C 2 [−1, 1] : v(±1) = 0}) L[φ] = φ (x) + λφ(x) − λφ(x) 1 −1 f (x, y)u(y)dy − λu(x) 1 −1 f (x, y)φ(y)dy, (1) where f ∈ L 2 ((...
متن کاملExistence 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 ·...
متن کاملExact multiplicity of solutions to a diffusive logistic equation with harvesting
An Ambrosetti-Prodi type exact multiplicity result is proved for a diffusive logistic equation with harvesting. We show that a modified diffusive logistic mapping has exactly either zero, or one, or two pre-images depending on the harvesting rate. It implies that the original diffusive logistic equation with harvesting has at most two positive steady state solutions.
متن کاملSpatial Dynamics of the Diffusive Logistic Equation with a Sedentary Compartment
We study an extension of the diffusive logistic equation or Fisher’s equation for a situation where one part of the population is sedentary and reproducing, and the other part migrating and subject to mortality. We show that this system is essentially equivalent to a semi-linear wave equation with viscous damping. With respect to persistence in bounded domains with absorbing boundary conditions...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1998
ISSN: 0022-247X
DOI: 10.1006/jmaa.1998.6044