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Other titles in the Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts series:
Applied Nonlinear Semigroups: An Introduction (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)by Adam Mcbride
Synopses & Reviews
Mathematical Methods in Practice Advisory Editors Bruno Brosowski Universit?t Frankfurt Germany Gary F. Roach University of Strathclyde UK Volume 3 Applied Nonlinear Semigroups A. Belleni-Morante University of Florence, Italy A. C. McBride University of Strathclyde, UK In many disciplines such as physics, chemistry, biology, meteorology, electronics and economics, it is increasingly necessary to develop mathematical models that describe how the state of a system evolves with time. A useful way of studying such a model is to recast the appropriate evolution equation as an Abstract Cauchy Problem (ACP), which can then be analysed via the powerful theory of semigroups of operators. The user-friendly presentation in the book is centred on Abstract Cauchy Problems which model various processes such as particle transport,diffusion and combustion, all of which are examples of systems which evolve with time. The authors provide an introduction to the requisite concepts from functional analysis before moving on to the theory of semigroups of linear operators and their application to linear ACPs. These ideas are then applied to semilinear problems and fully nonlinear problems and it is shown how results from the linear theory can be extended. Finally, a variety of applications of practical interest are included. By leading a non-expert to the solutions of problems involving evolution equations via the theory of semigroups of operators, both linear and nonlinear, the book provides an accessible introduction to the treatment of the subject. The reader is assumed to have a basic knowledge of real analysis and vector spaces. M.Sc. and graduate students of functional analysis, applied mathematics, physics and engineering will find this an invaluable introduction to the subject.
Book News Annotation:
The international duo of Bellini-Morante (U. of Florence, Italy) and McBride (U. of Strathclyde, Glasgow, Scotland) offer mathematical models for the numerous fields (e.g. physics, biology, meteorology, electronics, and economics) that need to describe the state of a system as it evolves over time. The authors overview the requisite concepts from functional analysis before moving on to the theory of semigroups of linear operators, and their applications to linear and nonlinear problems and the real world. Intended to be accessible to readers with familiarity with real analysis and vector spaces. Appendices feature Lebesgue integration and inequality proofs. Includes subject and symbol indexes. Annotation c. by Book News, Inc., Portland, OR (firstname.lastname@example.org)
In applied mathematics, nonlinear semigroups techniques often affect diverse problems ranging from modeling traffic flows, to neutron transport, to coagulation. This text introduces theory and application of semigroups of both linear and nonlinear operators used to develop mathematical models which monitor the status of systems over time.
Die erste gut verständliche, in sich geschlossene Einführung in Theorie und Anwendungen von Halbgruppen linearer und nichtlinearer Operatoren! Ein einführendes Kapitel erläutert die Grundlagen aus Funktionalanalysis und Theorie der Halbgruppen linearer und semilinearer Operatoren. An speziellere Kapitel schließen sich Anwendungsbeispiele aus der Praxis an. Übungsaufgaben helfen bei der Festigung des Stoffes.
Table of Contents
Spaces and Operators.
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