Overview
- Editors:
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Brian H. Gilding
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Department of Mathematics and Statistics College of Science, Sultan Qaboos University, Sultanate of Oman
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Robert Kersner
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Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary
- Describes a method leading to results which were otherwise unobtainable or are much sharper than those obtained previously
- Provides a reference work for applications of nonlinear diffusion, convection and reaction
- Brings together a large number of results – which have been obtained piecemeal in many different scientific disciplines – in a unifying framework
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Table of contents (13 chapters)
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- Brian H. Gilding, Robert Kersner
Pages 1-6
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- Brian H. Gilding, Robert Kersner
Pages 7-28
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- Brian H. Gilding, Robert Kersner
Pages 29-33
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- Brian H. Gilding, Robert Kersner
Pages 35-38
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- Brian H. Gilding, Robert Kersner
Pages 39-42
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- Brian H. Gilding, Robert Kersner
Pages 43-57
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- Brian H. Gilding, Robert Kersner
Pages 59-67
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- Brian H. Gilding, Robert Kersner
Pages 69-80
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- Brian H. Gilding, Robert Kersner
Pages 81-86
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- Brian H. Gilding, Robert Kersner
Pages 87-132
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- Brian H. Gilding, Robert Kersner
Pages 133-137
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- Brian H. Gilding, Robert Kersner
Pages 139-155
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- Brian H. Gilding, Robert Kersner
Pages 157-177
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Back Matter
Pages 179-210
About this book
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.
Editors and Affiliations
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Department of Mathematics and Statistics College of Science, Sultan Qaboos University, Sultanate of Oman
Brian H. Gilding
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Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary
Robert Kersner
