Traveling Wave Solutions of Parabolic Systems
Title | Traveling Wave Solutions of Parabolic Systems PDF eBook |
Author | A. I. Volpert |
Publisher | American Mathematical Soc. |
Pages | 474 |
Release | |
Genre | Mathematics |
ISBN | 9780821897577 |
The theory of travelling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. With introductory material accessible to non-mathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.
Traveling wave solutions of parabolic systems
Title | Traveling wave solutions of parabolic systems PDF eBook |
Author | Aĭzik Isaakovich Volʹpert |
Publisher | American Mathematical Society(RI) |
Pages | 448 |
Release | 1994 |
Genre | Chemical kinetics |
ISBN | 9780821846094 |
The theory of traveling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. The main part of the book contains original approaches developed by the authors. Among these are a description of the long-term behavior of the solutions by systems of waves; construction of rotations of vector fields for noncompact operators describing wave solutions; a proof of the existence of waves by the Leray-Schauder method; local, global, and nonlinear stability analyses for some classes of systems; and a determination of the wave velocity by the minimax method and the method of successive approximations. The authors show that wide classes of reaction-diffusion systems can be reduced to so-called monotone and locally monotone systems. This fundamental result allows them to apply the theory to combustion and chemical kinetics. With introductory material accessible to nonmathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.
Travelling-wave Solutions for Parabolic Systems
Title | Travelling-wave Solutions for Parabolic Systems PDF eBook |
Author | Elaine Craig Mackay Crooks |
Publisher | |
Pages | |
Release | 1996 |
Genre | |
ISBN |
Exact Traveling Wave Solutions of One-Dimensional Parabolic-Parabolic Models of Chemotaxis
Title | Exact Traveling Wave Solutions of One-Dimensional Parabolic-Parabolic Models of Chemotaxis PDF eBook |
Author | Maria Vladimirovna Shubina |
Publisher | |
Pages | 0 |
Release | 2020 |
Genre | Electronic books |
ISBN |
In this chapter we consider several different parabolic-parabolic systems of chemotaxis which depend on time and one space coordinate. For these systems we obtain the exact analytical solutions in terms of traveling wave variables. Not all of these solutions are acceptable for biological interpretation, but there are solutions that require detailed analysis. We find this interesting, since chemotaxis is present in the continuous mathematical models of cancer growth and invasion (Anderson, Chaplain, Lolas, et al.) which are described by the systems of reaction,Äìdiffusion-taxis partial differential equations, and the obtaining of exact solutions to these systems seems to be a very interesting task, and a more detailed analysis is possible in a future study.
Existence of Traveling Wave Solutions of Parabolic–parabolic Chemotaxis Systems
Title | Existence of Traveling Wave Solutions of Parabolic–parabolic Chemotaxis Systems PDF eBook |
Author | |
Publisher | |
Pages | |
Release | 2018 |
Genre | |
ISBN |
The Stability of Traveling Wave Solutions of Parabolic Equations
Title | The Stability of Traveling Wave Solutions of Parabolic Equations PDF eBook |
Author | Patrick Shawn Hagan |
Publisher | |
Pages | 678 |
Release | 1979 |
Genre | |
ISBN |
Traveling Wave Analysis of Partial Differential Equations
Title | Traveling Wave Analysis of Partial Differential Equations PDF eBook |
Author | Graham Griffiths |
Publisher | Academic Press |
Pages | 463 |
Release | 2010-12-09 |
Genre | Mathematics |
ISBN | 0123846536 |
Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors' intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net - Includes a spectrum of applications in science, engineering, applied mathematics - Presents a combination of numerical and analytical methods - Provides transportable computer codes in Matlab and Maple