Stationary patterns for a lotka-volterra cooperative model with a density-dependent diffusion term

Kazuhiro Oeda

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper is concerned with positive stationary solutions for a Lotka- Volterra cooperative model with a density-dependent diffusion term of a fractional type. The existence of stationary patterns is proven by the presence of density-dependent diffusion. Our proof is based on the Leray-Schauder degree theory and some a priori estimates. We also derive a certain limiting system which positive stationary solutions satisfy.

Original languageEnglish
Pages (from-to)93-112
Number of pages20
JournalFunkcialaj Ekvacioj
Volume52
Issue number1
DOIs
Publication statusPublished - 2009 Apr

Fingerprint

Lotka-Volterra
Stationary Solutions
Leray-Schauder Degree Theory
Positive Systems
Dependent
Term
A Priori Estimates
Fractional
Limiting
Model

Keywords

  • Cooperative model
  • Density-dependent diffusion
  • Leray-schauder degree theory
  • Limiting system
  • Stationary patterns

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Stationary patterns for a lotka-volterra cooperative model with a density-dependent diffusion term. / Oeda, Kazuhiro.

In: Funkcialaj Ekvacioj, Vol. 52, No. 1, 04.2009, p. 93-112.

Research output: Contribution to journalArticle

@article{9ae766a6880f4a15be8d2152cd895f5e,
title = "Stationary patterns for a lotka-volterra cooperative model with a density-dependent diffusion term",
abstract = "This paper is concerned with positive stationary solutions for a Lotka- Volterra cooperative model with a density-dependent diffusion term of a fractional type. The existence of stationary patterns is proven by the presence of density-dependent diffusion. Our proof is based on the Leray-Schauder degree theory and some a priori estimates. We also derive a certain limiting system which positive stationary solutions satisfy.",
keywords = "Cooperative model, Density-dependent diffusion, Leray-schauder degree theory, Limiting system, Stationary patterns",
author = "Kazuhiro Oeda",
year = "2009",
month = "4",
doi = "10.1619/fesi.52.93",
language = "English",
volume = "52",
pages = "93--112",
journal = "Funkcialaj Ekvacioj",
issn = "0532-8721",
publisher = "Mathematical Society of Japan - Kobe University",
number = "1",

}

TY - JOUR

T1 - Stationary patterns for a lotka-volterra cooperative model with a density-dependent diffusion term

AU - Oeda, Kazuhiro

PY - 2009/4

Y1 - 2009/4

N2 - This paper is concerned with positive stationary solutions for a Lotka- Volterra cooperative model with a density-dependent diffusion term of a fractional type. The existence of stationary patterns is proven by the presence of density-dependent diffusion. Our proof is based on the Leray-Schauder degree theory and some a priori estimates. We also derive a certain limiting system which positive stationary solutions satisfy.

AB - This paper is concerned with positive stationary solutions for a Lotka- Volterra cooperative model with a density-dependent diffusion term of a fractional type. The existence of stationary patterns is proven by the presence of density-dependent diffusion. Our proof is based on the Leray-Schauder degree theory and some a priori estimates. We also derive a certain limiting system which positive stationary solutions satisfy.

KW - Cooperative model

KW - Density-dependent diffusion

KW - Leray-schauder degree theory

KW - Limiting system

KW - Stationary patterns

UR - http://www.scopus.com/inward/record.url?scp=71949109426&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71949109426&partnerID=8YFLogxK

U2 - 10.1619/fesi.52.93

DO - 10.1619/fesi.52.93

M3 - Article

AN - SCOPUS:71949109426

VL - 52

SP - 93

EP - 112

JO - Funkcialaj Ekvacioj

JF - Funkcialaj Ekvacioj

SN - 0532-8721

IS - 1

ER -