Shock Waves and Reaction-Diffusion Equations.

反应扩散系统 休克(循环) 冲击波 扩散 物理 机械 热力学 医学 内科学
作者
Barbara Lee Keyfitz,Joel Smoller
出处
期刊:American Mathematical Monthly [Taylor & Francis]
卷期号:93 (4): 315-315 被引量:37
标识
DOI:10.2307/2323701
摘要

For this edition, a number of typographical errors and minor slip-ups have been corrected.In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results."This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition.Section I deals with reaction-diffusion equations, and in it are described both the work of C.Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations.Section II deals with some recent results in shock-wave theory.The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P.Liu's work on the stability of viscous profiles for shock waves.In the next section, Conley's connection index and connection matrix are described; these general notions are useful in constructing travelling waves for systems of nonlinear equations.The final section, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves.Their theory is general enough to be applicable to many interesting reaction-diffusion systems.Many people have been kind in assisting me with this revision; in particular, special thanks are due to Bob Gardner, Xabier Garaizer, David Hoff, Chen Jing, Tai-Ping Liu, Blake Temple, Rick Wasserman, Zhou-Ping Xin, and especially to Vijay.Pant for his careful reading of the manuscript.In addition, I received many letters from mathematicians all over the world, who either corrected some of my errors, or showed me "different proofs."I wish to thank all of them for their interest.In closing, I want to dedicate this edition to the memory of both Charles Conley and Edward Conway.I This is not quite true; there are some good survey articles on shock waves (e.g., [Lx 5]) but these do not contain many proofs.Also in the theory of reaction -diffusion equations, there are the books [Pi] and [Mu], but they both seem to me to be research monographs.
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
PDF的下载单位、IP信息已删除 (2025-6-4)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
罗亚亚完成签到,获得积分10
刚刚
1秒前
昏睡的蟠桃应助天气好好采纳,获得50
2秒前
CodeCraft应助sjy采纳,获得10
2秒前
scichu完成签到,获得积分20
3秒前
3秒前
3秒前
zk_orange发布了新的文献求助10
5秒前
搜集达人应助呆萌冷风采纳,获得10
7秒前
7秒前
cnm发布了新的文献求助10
8秒前
8秒前
8秒前
生产队的LV完成签到,获得积分10
10秒前
清脆香萱完成签到,获得积分10
13秒前
13秒前
白色风车发布了新的文献求助10
13秒前
HORSE047发布了新的文献求助10
13秒前
赘婿应助Coco采纳,获得10
13秒前
chenxi完成签到 ,获得积分10
14秒前
Lucas应助EthanChan采纳,获得10
14秒前
量子星尘发布了新的文献求助10
15秒前
33发布了新的文献求助10
16秒前
外向从灵发布了新的文献求助10
16秒前
呼呼呼完成签到,获得积分10
16秒前
16秒前
闪闪的发布了新的文献求助10
16秒前
ED应助香香采纳,获得10
17秒前
小马甲应助香香采纳,获得10
17秒前
18秒前
祎薇完成签到,获得积分10
18秒前
大模型应助白色风车采纳,获得10
19秒前
李健的小迷弟应助Zj采纳,获得10
19秒前
xiangjun完成签到,获得积分10
20秒前
20秒前
attilio发布了新的文献求助30
21秒前
ll发布了新的文献求助200
23秒前
外向从灵完成签到,获得积分10
24秒前
熙若白完成签到,获得积分10
25秒前
HORSE047完成签到,获得积分10
25秒前
高分求助中
The Mother of All Tableaux Order, Equivalence, and Geometry in the Large-scale Structure of Optimality Theory 2400
Ophthalmic Equipment Market by Devices(surgical: vitreorentinal,IOLs,OVDs,contact lens,RGP lens,backflush,diagnostic&monitoring:OCT,actorefractor,keratometer,tonometer,ophthalmoscpe,OVD), End User,Buying Criteria-Global Forecast to2029 2000
Cognitive Neuroscience: The Biology of the Mind 1000
Cognitive Neuroscience: The Biology of the Mind (Sixth Edition) 1000
Optimal Transport: A Comprehensive Introduction to Modeling, Analysis, Simulation, Applications 800
Official Methods of Analysis of AOAC INTERNATIONAL 600
ACSM’s Guidelines for Exercise Testing and Prescription, 12th edition 588
热门求助领域 (近24小时)
化学 材料科学 医学 生物 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 遗传学 基因 物理化学 催化作用 冶金 细胞生物学 免疫学
热门帖子
关注 科研通微信公众号,转发送积分 3958225
求助须知:如何正确求助?哪些是违规求助? 3504388
关于积分的说明 11118283
捐赠科研通 3235682
什么是DOI,文献DOI怎么找? 1788411
邀请新用户注册赠送积分活动 871211
科研通“疑难数据库(出版商)”最低求助积分说明 802565