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Travelling Waves in Nonlinear Diffusion-Convection Reaction

  • Brian H. Gilding
  • Robert Kersner

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 60)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Brian H. Gilding, Robert Kersner
    Pages 1-6
  3. Brian H. Gilding, Robert Kersner
    Pages 7-28
  4. Brian H. Gilding, Robert Kersner
    Pages 29-33
  5. Brian H. Gilding, Robert Kersner
    Pages 35-38
  6. Brian H. Gilding, Robert Kersner
    Pages 39-42
  7. Brian H. Gilding, Robert Kersner
    Pages 43-57
  8. Brian H. Gilding, Robert Kersner
    Pages 59-67
  9. Brian H. Gilding, Robert Kersner
    Pages 69-80
  10. Brian H. Gilding, Robert Kersner
    Pages 81-86
  11. Brian H. Gilding, Robert Kersner
    Pages 87-132
  12. Brian H. Gilding, Robert Kersner
    Pages 133-137
  13. Brian H. Gilding, Robert Kersner
    Pages 139-155
  14. Brian H. Gilding, Robert Kersner
    Pages 157-177
  15. Back Matter
    Pages 179-210

About this book

Introduction

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.

Keywords

Genetics Partial Differential Equations Population Dynamics Travelling Waves evolution partial differential equation

Editors and affiliations

  • Brian H. Gilding
    • 1
  • Robert Kersner
    • 2
  1. 1.Department of Mathematics and Statistics College of ScienceSultan Qaboos UniversitySultanate of Oman
  2. 2.Computer and Automation Research InstituteHungarian Academy of SciencesBudapestHungary

Bibliographic information