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Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations. The book is comprised of five chapters that feature the following: A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications * Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime * Geometric and diffractive optics, including wave interactions Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations. Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable
The aim of this Handbook is to acquaint the reader with the current
status of the theory of evolutionary partial differential
equations, and with some of its applications. Evolutionary partial
differential equations made their first appearance in the 18th
century, in the endeavor to understand the motion of fluids and
other continuous media. The active research effort over the span of
two centuries, combined with the wide variety of physical phenomena
that had to be explained, has resulted in an enormous body of
literature. Any attempt to produce a comprehensive survey would be
futile. The aim here is to collect review articles, written by
leading experts, which will highlight the present and expected
future directions of development of the field. The emphasis will be
on nonlinear equations, which pose the most challenging problems
today.
The material collected in this volume discusses the present as well
as expected future directions of development of the field with
particular emphasis on applications. The seven survey articles
present different topics in Evolutionary PDE s, written by leading
experts.
The material collected in this volume reflects the active present
of this area of mathematics, ranging from the abstract theory of
gradient flows to stochastic representations of non-linear
parabolic PDE's.
This volume is an outcome of the EQUADIFF 87 conference in Greece. It addresses a wide spectrum of topics in the theory and applications of differential equations, ordinary, partial, and functional. The book is intended for mathematics and scientists.
This book contains several introductory texts concerning the main
directions in the theory
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