Standing pulse-like solutions of a spatially aggregating population model

DOI10.1007/BF03167041zbMath0587.92024MaRDI QIDQ3714948

Tsutomu Ikeda

Publication date: 1985

Published in: Japan Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

positive solutionsfree boundary problemstationary solutionsnonlocal interactiondensity-dependent dispersalnonlinear degenerate diffusion equationpulse-like solutionseigenvalue problem of differential-difference typenonlocal convection termspatially aggregating population model

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Ecology (92D40) Initial value problems for linear higher-order PDEs (35G10) Parabolic equations and parabolic systems (35K99) Higher-order parabolic equations (35K25) Qualitative properties of solutions to partial differential equations (35B99)

Related Items (7)

A nonlocal continuum model for biological aggregation ⋮ Stability of localized stationary solutions ⋮ Wellposedness and regularity of solutions of an aggregation equation ⋮ Local and Global Existence for an Aggregation Equation ⋮ Finite-time singularities of an aggregation equation in \(\mathbb R^n\) with fractional dissipation ⋮ Refined blowup criteria and nonsymmetric blowup of an aggregation equation ⋮ Stationary States and Asymptotic Behavior of Aggregation Models with Nonlinear Local Repulsion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some nonlinear degenerate diffusion equations related to population dynamics
• Numerical approximations to interface curves for a porous media equation
• Model for chemotaxis
• Some nonlinear degenerate diffusion equations with a nonlocally convective term in ecology
• On a mathematical model describing the aggregation of amoebae
• The Cauchy problem for an equation in the theory of infiltration
• On the diffusion of biological populations
• Properties of solutions of an equation in the theory of infiltration
• Regularity properties of flows through porous media: The interface
• Liquid Instability and Freezing –Reductive Perturbation Approach–
• Asymptotic Behavior for a Nonlinear Degenerate Diffusion Equation in Population Dynamics
• Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations
• An Interface Tracking Algorithm for the Porous Medium Equation
• A numerical approach to interface curves for some nonlinear diffusion equations
• Degenerate diffusion equations with drift functionals modelling aggregation
• A Linearly Implicit Finite-Difference Scheme for the One-Dimensional Porous Medium Equation
• Continuity of the Density of a Gas Flow in a Porous Medium
• Regularity of the Free Boundary for the One-Dimensional Flow of Gas in a Porous Medium
• The Porous Medium Equation in One Dimension
• Asymptotic Behavior of the interfaces to a nonlinear degenerate diffusion equation in population dynamics
• Regularity Propeties of Flows Through Porous Media
• A Finite Difference Approach to Some Degenerate Nonlinear Parabolic Equations
• Regularity Properties of Flows Through Porous Media: A Counterexample
• DIFFUSION FROM AN INSTANTANEOUS POINT SOURCE WITH A CONCENTRATION-DEPENDENT COEFFICIENT
• Functional differential equations

This page was built for publication: Standing pulse-like solutions of a spatially aggregating population model