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Applied Nonlinear Semigroups (Hardcover)
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Applied Nonlinear Semigroups (Hardcover)
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Mathematical Methods in Practice Advisory Editors Bruno Brosowski
UniversitAt 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.
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