On bounded positive stationary solutions for a nonlocal Fisher-KPP equation

DOI10.1016/j.na.2014.09.004zbMath1303.35006arXiv1307.3480OpenAlexW2164638364MaRDI QIDQ468607

Franz Achleitner, Christian Kuehn

Publication date: 7 November 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.3480

zbMATH Keywords

perturbation theoryweighted Sobolev spacesteady statestationary solutionimplicit function theoremFisher-KPP equationFKPPnonlocal convolution operator

Mathematics Subject Classification ID

Second-order elliptic equations (35J15)

Related Items (10)

Validity of amplitude equations for nonlocal nonlinearities ⋮ A meeting point of entropy and bifurcations in cross-diffusion herding ⋮ The Swift-Hohenberg equation with a nonlocal nonlinearity ⋮ Pattern formation in the doubly-nonlocal Fisher-KPP equation ⋮ An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher–KPP equation ⋮ An approximation solvability method for nonlocal semilinear differential problems in Banach spaces ⋮ Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical systems approach ⋮ A non-local perturbation of the logistic equation in \(\mathbb{R}^N\) ⋮ Markov evolutions in spatial ecology: from microscopic dynamics to kinetics ⋮ A gradient flow formulation for the stochastic Amari neural field model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation
• On the existence of stationary solutions for some non-Fredholm integro-differential equations
• Positive stationary solutions and spreading speed of KPP equations in locally spatially inhomogeneous media
• Rapid traveling waves in the nonlocal Fisher equation connect two unstable states
• Local vs. non-local interactions in population dynamics
• The maximum principle
• Non-existence of positive solutions of fully nonlinear elliptic equations in unbounded domains
• On the origin of tiger bush
• Front propagation in reactive systems with anomalous diffusion
• Travelling fronts for the KPP equation with spatio-temporal delay
• Mathematical biology. Vol. 1: An introduction.
• Propagation speed of travelling fronts in non local reaction-diffusion equations
• The speed of propagation for KPP type problems. I: Periodic framework
• Delay induced traveling wave fronts in reaction diffusion equations of KPP-Fisher type
• Sobolev spaces and elliptic theory on unbounded domains in \(\mathbb{R}^n\)
• Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay
• Analysis of the periodically fragmented environment model. I: Species persistence
• Front propagation for a jump process model arising in spacial ecology
• Concentration in the Nonlocal Fisher Equation: the Hamilton-Jacobi Limit
• Fast Propagation for Fractional KPP Equations with Slowly Decaying Initial Conditions
• Wave-like Solutions for Nonlocal Reaction-diffusion Equations: a Toy Model
• Solutions of Laplace Equation in n -Dimensional Spaces
• On the nonlocal Fisher–KPP equation: steady states, spreading speed and global bounds
• Concrete Functional Calculus
• Monotone wavefronts of the nonlocal Fisher–KPP equation
• LOGISTIC TYPE EQUATIONS ON ℝ^N BY A SQUEEZING METHOD INVOLVING BOUNDARY BLOW-UP SOLUTIONS
• Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
• The speed of propagation for KPP type problems. II: General domains
• The non-local Fisher–KPP equation: travelling waves and steady states
• On invertibility of linear partial differential operators in Hölder and Sobolev spaces
• Spatial Structures and Periodic Travelling Waves in an Integro-Differential Reaction-Diffusion Population Model
• On a non-local equation arising in population dynamics
• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
• Travelling front solutions of a nonlocal Fisher equation

This page was built for publication: On bounded positive stationary solutions for a nonlocal Fisher-KPP equation