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Hyperbolic and viscous conservation laws

Liu, Tai-ping



Hyperbolic and viscous conservation laws

Tác giả: Liu, Tai-ping
Loại tài liệu: Sách, chuyên khảo, tuyển tập
Ký hiệu: Lv3868
Mã giá: 35LI
Nội dung tóm tắt: Xem chi tiết
There has been intense interest in recent years in the study of shock waves in various physical situations: nonlinear elasticity, magnetohydrodynamics, multiphase flows, combustion, etc., in addition to the classical gas dynamics shocks. The purpose of this study is to understand, physically and mathematically, the new wave phenomena. These issues are very interesting because of the strongly nonlinear effects. The central issue is the understanding of nonlinear wave interactions. I have presented in this book, for the first time, the in-depth analysis of wave interactions for general systems of hyperbolic and viscous conservation laws. The book starts with the basic ideas of shock wave theory and is suitable for graduate students interested in an introduction to this vital area of nonlinear analysis. The book is also aimed at researchers who are interested in, nonlinear waves in general and would like to become familiarized with the analytical techniques that have been introduced, some in the last few years, for the qualitative theory of shock waves. I will discuss the existence, regularity, and large-time behavior of solutions for hyperbolic conservation laws. The main tools are the random choice method and the wave tracing technique. For viscous conservation laws, I have included the recent analysis of dissipation, compression, and expansion waves. Energy and pointwise estimates are the main analytical techniques. The main theme of these two studies is the treatment of nonlinear interaction of waves. I will start with the scalar conservation law to illustrate the elementary notions of weak solutions and entropy conditions. For viscous conservation laws, I will start with the Burgers equation to understand the coupling of nonlinear flux and dissipation.
Mục lục: Xem chi tiết
Chapter 1. Hyperbolic Conservation Laws 1.1 Preliminaries 1.2 Riemann Problem 1.3 Wave Interactions 1.4 Random Choice Method 1.5 Nonlinear Superposition 1.6 Large-Time Behavior and Regularity Chapter 2. Viscous Conservation Laws 2.1 Preliminaries 2.2 The Burgers Equation 2.3 Diffusion Waves 2.4 Viscous Shocks 2.5 Viscous Rarefaction Waves 2.6 Concluding Remarks Bibliography Index

Thông tin chi tiết

    Dạng tài liệu:Bản in
    Chỉ số ISBN:0-89871-436-2
    Ngôn ngữ:eng
    Mã giá:35LI
    Mã MSC:Đang cập nhật ...
    Tác giả:Liu, Tai-ping
    Nhan đề:Hyperbolic and viscous conservation laws
    Xuất bản, phát hành:H : Philadelphia , 2000
    Số trang:73;
    Kích thước:24 cm
    Từ Khóa:diffusion waves , entropy solution , rarefaction waves , stability of nonlinear waves , wave interactions
    Bộ sách:CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 72

Thông tin xếp giá

  • ĐKCB: 3545020059760
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