Applications of Symmetry Methods to Partial Differential Equations (Current Topics in Microbiology & Immunology)

Bluman, George, Cheviakov, Alexei, Anco, Stephen

ISBN 10: 0387571930 / ISBN 13: 9780387571935

Published by Springer, 2011

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Bibliographic Details

• Title: Applications of Symmetry Methods to Partial Differential Equations (Current Topics in Microbiology & Immunology)
• Publisher: Springer
• Publication Date: 2011
• ISBN 10: 0387571930
• ISBN 13: 9780387571935
• Binding: Paperback
• Condition: Like New
• Book Type: book

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Synopsis

The etiologic involvement of specific human papillomavirus (HPV) types in cancer of the cervix and their role in a substantial proportion of other anogenital cancers and cancers of the oropharynx (most prominently cancers of the tonsils and of the larynx) label HPV as a prime target for the analysis of mechanisms leading to the development of malignant tumors in humans. As in other viral infections linked to human cancers, HPV infection is not sufficient for the induction of malignant growth. It emerges, however, as the main factor, introducing new genes into the latently infected cells whose function as oncogenes have become clearly established during the past few years. The regulation of their expression by specific host cell proteins, stimulated by intra- and intercellular signals, seems to represent a primary defense mechanism against the induction of unrestricted growth. The failure of this host cell control system, on the other hand, by mutational changes affecting the host cell genome appears to predispose for malignant conversion. This volume summarizes various aspects of HPV research and its relationship to human cancers and provides an overview of current topics in an exciting research field.

From the Back Cover

This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether’s theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful.

This book is a sequel to Symmetry and Integration Methods for Differential Equations (2002) by George W. Bluman and Stephen C. Anco. The emphasis in the present book is on how to find systematically symmetries (local and nonlocal) and conservation laws (local and nonlocal) of a given PDE system and how to use systematically symmetries and conservation laws for related applications.