Travelling Waves in Nonlinear Diffusion-Convection Reaction

Brian H. Gilding, Robert Kersner (Autoren)

Buch | Hardcover

IX, 210 Seiten

2004
Springer Basel (Verlag)
978-3-7643-7071-8 (ISBN)

Artikel merken

This monograph has grown out of research we started in 1987, although the foun dations were laid in the 1970's when both of us were working on our doctoral theses, trying to generalize the now classic paper of Oleinik, Kalashnikov and Chzhou on nonlinear degenerate diffusion. Brian worked under the guidance of Bert Peletier at the University of Sussex in Brighton, England, and, later at Delft University of Technology in the Netherlands on extending the earlier mathematics to include nonlinear convection; while Robert worked at Lomonosov State Univer sity in Moscow under the supervision of Anatolii Kalashnikov on generalizing the earlier mathematics to include nonlinear absorption. We first met at a conference held in Rome in 1985. In 1987 we met again in Madrid at the invitation of Ildefonso Diaz, where we were both staying at 'La Residencia'. As providence would have it, the University 'Complutense' closed down during this visit in response to student demonstra tions, and, we were very much left to our own devices. It was natural that we should gravitate to a research topic of common interest. This turned out to be the characterization of the phenomenon of finite speed of propagation for nonlin ear reaction-convection-diffusion equations. Brian had just completed some work on this topic for nonlinear diffusion-convection, while Robert had earlier done the same for nonlinear diffusion-absorption. There was no question but that we bundle our efforts on the general situation.

1 Introduction.- 2 General theory.- 2.1 Basic hypotheses.- 2.2 Integral equation theory.- 2.3 Proof of equivalence.- 2.4 Illustration of difficulties.- 2.5 Further properties.- 2.6 Classical results.- Bibliographical notes.- 3 Transformations.- Bibliographical notes.- 4 Travelling waves.- 4.1 Admissible wave speeds.- 4.2 Number of solutions.- Bibliographical notes.- 5 Convection-diffusion.- Bibliographical notes.- 6 Reaction-diffusion.- 6.1 Sink term.- 6.2 Source term.- 6.3 Smooth coefficients.- Bibliographical notes.- 7 Power-law equations.- Bibliographical notes.- 8 Wavefronts.- 8.1 Admissible wave speeds.- 8.2 Number of wavefronts.- 8.3 Illustrations.- 8.4 Multiple equilibria.- Bibliographical notes.- 9 Wavefronts for convection-diffusion.- Bibliographical notes.- 10 Wavefronts for reaction-diffusion.- 10.1 Fixed sign.- 10.2 One sign change.- 10.3 Smooth coefficients.- Bibliographical notes.- 11 Unbounded waves.- 12 Wavefronts and unbounded waves for power-law equations.- 12.1 Convection-diffusion.- 12.2 Reaction-diffusion with linear convection.- 12.3 Reaction-convection-diffusion.- Bibliographical notes.- 13 Explicit travelling-wave solutions.- 13.1 Power-law equations.- 13.2 Generalizations of the Fisher equation.- 13.3 Generating further explicit solutions.- Bibliographical notes.

Erscheint lt. Verlag	23.7.2004
Reihe/Serie	Progress in Nonlinear Differential Equations and Their Applications
Zusatzinfo	IX, 210 p.
Verlagsort	Basel
Sprache	englisch
Maße	155 x 235 mm
Gewicht	505 g
Themenwelt	Informatik ► Weitere Themen ► Bioinformatik
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Biologie ► Evolution
Schlagworte	Differenzialgleichungen • Evolution • Genetics • partial differential equation • Partial differential equations • population dynamics • Travelling Waves
ISBN-10	3-7643-7071-8 / 3764370718
ISBN-13	978-3-7643-7071-8 / 9783764370718
Zustand	Neuware