On the existence of traveling waves for delayed reaction-diffusion equations

Haiyan Wang

doi:10.1016/j.jde.2009.04.002

On the existence of traveling waves for delayed reaction-diffusion equations

Haiyan Wang

Mathematical and Natural Sciences, School of (SMNS)

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

53 Scopus citations

Abstract

We study the existence of traveling wave solutions for reaction-diffusion equations with nonlocal delay, where reaction terms are not necessarily monotone. The existence of traveling wave solutions for reaction-diffusion equations with nonlocal delays is obtained by combining upper and lower solutions for associated integral equations and the Schauder fixed point theorem. The smoothness of upper and lower solutions is not required in this paper.

Original language	English (US)
Pages (from-to)	887-905
Number of pages	19
Journal	Journal of Differential Equations
Volume	247
Issue number	3
DOIs	https://doi.org/10.1016/j.jde.2009.04.002
State	Published - Aug 1 2009

Keywords

Delay
Schauder fixed point theorem
Traveling waves

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jde.2009.04.002

Cite this

@article{94027c8462224808ac6df17e7ab484b5,

title = "On the existence of traveling waves for delayed reaction-diffusion equations",

abstract = "We study the existence of traveling wave solutions for reaction-diffusion equations with nonlocal delay, where reaction terms are not necessarily monotone. The existence of traveling wave solutions for reaction-diffusion equations with nonlocal delays is obtained by combining upper and lower solutions for associated integral equations and the Schauder fixed point theorem. The smoothness of upper and lower solutions is not required in this paper.",

keywords = "Delay, Schauder fixed point theorem, Traveling waves",

author = "Haiyan Wang",

note = "Funding Information: Supported by a SRCA grant from the New College of Interdisciplinary Arts and Sciences at Arizona State University. E-mail address: wangh@asu.edu.",

year = "2009",

month = aug,

day = "1",

doi = "10.1016/j.jde.2009.04.002",

language = "English (US)",

volume = "247",

pages = "887--905",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "3",

}

TY - JOUR

T1 - On the existence of traveling waves for delayed reaction-diffusion equations

AU - Wang, Haiyan

N1 - Funding Information: Supported by a SRCA grant from the New College of Interdisciplinary Arts and Sciences at Arizona State University. E-mail address: wangh@asu.edu.

PY - 2009/8/1

Y1 - 2009/8/1

N2 - We study the existence of traveling wave solutions for reaction-diffusion equations with nonlocal delay, where reaction terms are not necessarily monotone. The existence of traveling wave solutions for reaction-diffusion equations with nonlocal delays is obtained by combining upper and lower solutions for associated integral equations and the Schauder fixed point theorem. The smoothness of upper and lower solutions is not required in this paper.

AB - We study the existence of traveling wave solutions for reaction-diffusion equations with nonlocal delay, where reaction terms are not necessarily monotone. The existence of traveling wave solutions for reaction-diffusion equations with nonlocal delays is obtained by combining upper and lower solutions for associated integral equations and the Schauder fixed point theorem. The smoothness of upper and lower solutions is not required in this paper.

KW - Delay

KW - Schauder fixed point theorem

KW - Traveling waves

UR - http://www.scopus.com/inward/record.url?scp=67349212966&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349212966&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2009.04.002

DO - 10.1016/j.jde.2009.04.002

M3 - Article

AN - SCOPUS:67349212966

SN - 0022-0396

VL - 247

SP - 887

EP - 905

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 3

ER -

On the existence of traveling waves for delayed reaction-diffusion equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this