Traveling wave solutions of a reaction-diffusion equation with state-dependent delay

Guo Lin; Haiyan Wang

doi:10.3934/cpaa.2016.15.319

Traveling wave solutions of a reaction-diffusion equation with state-dependent delay

Guo Lin, Haiyan Wang

Mathematical and Natural Sciences, School of (SMNS)

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established. When the birth function is not monotone, the minimal wave speed of nontrivial traveling wave solutions is obtained. The results are proved by the construction of upper and lower solutions and application of the fixed point theorem.

Original language	English (US)
Pages (from-to)	319-334
Number of pages	16
Journal	Communications on Pure and Applied Analysis
Volume	15
Issue number	2
DOIs	https://doi.org/10.3934/cpaa.2016.15.319
State	Published - Mar 1 2016

Keywords

Asymptotic spreading
Comparison principle
Minimal wave speed

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.3934/cpaa.2016.15.319

Cite this

@article{79dbfa13465246a4811329dd7ac044da,

title = "Traveling wave solutions of a reaction-diffusion equation with state-dependent delay",

abstract = "This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established. When the birth function is not monotone, the minimal wave speed of nontrivial traveling wave solutions is obtained. The results are proved by the construction of upper and lower solutions and application of the fixed point theorem.",

keywords = "Asymptotic spreading, Comparison principle, Minimal wave speed",

author = "Guo Lin and Haiyan Wang",

note = "Funding Information: The authors would like to thank the anonymous referee for several suggestions that greatly improve the expression in the paper. Guo Lin is grateful to Professor Xingfu Zou for his very valuable comments and suggestions. Guo Lin is supported by NSF of China (grant 11471149), Haiyan Wang is supported by NSF of China (grant 11571324). Publisher Copyright: {\textcopyright} 2016, American Institute of Mathematical Sciences. All rights reserved.",

year = "2016",

month = mar,

day = "1",

doi = "10.3934/cpaa.2016.15.319",

language = "English (US)",

volume = "15",

pages = "319--334",

journal = "Communications on Pure and Applied Analysis",

issn = "1534-0392",

publisher = "American Institute of Mathematical Sciences",

number = "2",

}

TY - JOUR

T1 - Traveling wave solutions of a reaction-diffusion equation with state-dependent delay

AU - Lin, Guo

AU - Wang, Haiyan

N1 - Funding Information: The authors would like to thank the anonymous referee for several suggestions that greatly improve the expression in the paper. Guo Lin is grateful to Professor Xingfu Zou for his very valuable comments and suggestions. Guo Lin is supported by NSF of China (grant 11471149), Haiyan Wang is supported by NSF of China (grant 11571324). Publisher Copyright: © 2016, American Institute of Mathematical Sciences. All rights reserved.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established. When the birth function is not monotone, the minimal wave speed of nontrivial traveling wave solutions is obtained. The results are proved by the construction of upper and lower solutions and application of the fixed point theorem.

AB - This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established. When the birth function is not monotone, the minimal wave speed of nontrivial traveling wave solutions is obtained. The results are proved by the construction of upper and lower solutions and application of the fixed point theorem.

KW - Asymptotic spreading

KW - Comparison principle

KW - Minimal wave speed

UR - http://www.scopus.com/inward/record.url?scp=85009765460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009765460&partnerID=8YFLogxK

U2 - 10.3934/cpaa.2016.15.319

DO - 10.3934/cpaa.2016.15.319

M3 - Article

AN - SCOPUS:85009765460

SN - 1534-0392

VL - 15

SP - 319

EP - 334

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 2

ER -

Traveling wave solutions of a reaction-diffusion equation with state-dependent delay

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this