Transversality in scalar reaction-diffusion equations on a circle

被引：14

作者：

Czaja, Radoslaw ^{[1
,2
]}

Rocha, Carlos ^{[1
]}

机构：

[1] Inst Super Tecn, Dept Matemat, Ctr Anal Matemat Geometria & Sistemas Dinam, P-1049001 Lisbon, Portugal

[2] Silesian Univ, Inst Math, PL-40007 Katowice, Poland

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2008年 / 245卷 / 03期

关键词：

periodic orbit; heteroclinic orbit; transversality; global attractor; zero number;

D O I：

10.1016/j.jde.2008.01.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that stable and unstable manifolds of hyperbolic periodic orbits for general scalar reaction-diffusion equations on a circle always intersect transversally. The argument also shows that for a periodic orbit there are no homoclinic connections. The main tool used in the proofs is Matano's zero number theory dealing with the Sturm nodal properties of the solutions. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：692 / 721

页数：30

共 50 条

[21] COUPLED REACTION-DIFFUSION EQUATIONS
FREIDLIN, M
[J]. ANNALS OF PROBABILITY, 1991, 19 (01): : 29 - 57
[22] Fractional reaction-diffusion equations
Saxena, R. K.
Mathai, A. M.
Haubold, H. J.
[J]. ASTROPHYSICS AND SPACE SCIENCE, 2006, 305 (03) : 289 - 296
[23] The evolution of reaction-diffusion waves in a class of scalar reaction-diffusion equations. Initial data with exponential decay rates or compact support
Leach, JA
Needham, DJ
Kay, AL
[J]. QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 2003, 56 : 217 - 249
[24] ON THE SOLUTION OF REACTION-DIFFUSION EQUATIONS
HILL, JM
[J]. IMA JOURNAL OF APPLIED MATHEMATICS, 1981, 27 (02) : 177 - 194
[25] Fractional Reaction-Diffusion Equations
R. K. Saxena
A. M. Mathai
H. J. Haubold
[J]. Astrophysics and Space Science, 2006, 305 : 289 - 296
[26] Planar and screw-shaped solutions for a system of two reaction-diffusion equations on the circle
Bueger, Matthias
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2006, 16 (04) : 745 - 756
[27] Transversality in semilinear parabolic equations on the circle
Rocha, C
[J]. EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS, 2005, : 672 - 677
[28] Large-time solutions of a class of scalar, nonlinear hyperbolic reaction-diffusion equations
Leach, J. A.
Bassom, Andrew P.
[J]. JOURNAL OF ENGINEERING MATHEMATICS, 2021, 130 (01)
[29] The Motion Law of Fronts for Scalar Reaction-diffusion Equations with Multiple Wells: the Degenerate Case
Bethuel, Fabrice
Smets, Didier
[J]. PARTIAL DIFFERENTIAL EQUATIONS ARISING FROM PHYSICS AND GEOMETRY: A VOLUME IN MEMORY OF ABBAS BAHRI, 2019, 450 : 88 - 171
[30] Sharp Estimates for the Global Attractor of Scalar Reaction-Diffusion Equations with a Wentzell Boundary Condition
Gal, Ciprian G.
[J]. JOURNAL OF NONLINEAR SCIENCE, 2012, 22 (01) : 85 - 106

← 1 2 3 4 5 →