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Full Description
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
Contents
1. Shallow-Water Equations and Related Topics
2. Fast Reaction Limit of Competition-Diffusion Systems
3. The Mathematics of Nonlinear Optics
4. Thermoelasticity
5. Unique Continuation Properties and Quantitative Estimates of Unique Continuation for Parabolic Equations
