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This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations. The first three chapters form a comprehensive survey of most modern contributions also describing in detail the mathematical properties of each model. Acceleration waves and shock waves are the focus in the next two chapters. Numerical techniques, continuous data dependence, and spatial stability of the solution in a cylinder, feature prominently among other topics treated in the following two chapters. The final two chapters are devoted to a description of selected applications and the corresponding formation of mathematical models. Illustrations are taken from a broad range that includes nanofluids, porous media, thin films, nuclear reactors, traffic flow, biology, and medicine, all of contemporary active technological importance and interest.
This book will be of value to applied mathematicians, theoretical engineers and other practitioners who wish to know both the theory and its relevance to diverse applications.
List of contents
Preface.-Introduction.- Interaction with elasticity.-Interaction with fluids.-Acceleration waves.-Shock waves.-Numerical solutions.-Qualitative estimates.-Spatial decay.-Nanofluids.-Other applications.-References.
About the author
Brian Straughan's research is in partial differential equations, scientific computing, and their applications to problems in the real world.
Summary
This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations. The first three chapters form a comprehensive survey of most modern contributions also describing in detail the mathematical properties of each model. Acceleration waves and shock waves are the focus in the next two chapters. Numerical techniques, continuous data dependence, and spatial stability of the solution in a cylinder, feature prominently among other topics treated in the following two chapters. The final two chapters are devoted to a description of selected applications and the corresponding formation of mathematical models. Illustrations are taken from a broad range that includes nanofluids, porous media, thin films, nuclear reactors, traffic flow, biology, and medicine, all of contemporary active technological importance and interest.
This book will be of value to applied mathematicians, theoretical engineers and other practitioners who wish to know both the theory and its relevance to diverse applications.
Report
From the reviews:
"The purpose of the present book ... is to discuss from both physical and mathematical viewpoints the various proposals of generalization of Fourier's conduction law as to render the heat propagation equation in some hyperbolic form. ... this book, with its rich references and rigorous mathematics, provides an invaluable synthesis on the subject matter ... . It belongs on the shelf of all graduate students, scientists and engineers interested in thermal waves." (Gérard A. Maugin, Journal of Thermal Stresses, Vol. 37 (3), 2014)
"The presentation of the material is clear and consequential, and reading it is pleasant. The book can be useful for scholars working in continuum thermodynamics and applied mathematics. It can be chosen as a textbook for some graduate courses or in Ph.D. programs in applied mathematics or mathematical engineering. The exercises at the end of Chapters ... are useful didactic additions." (Paolo Maria Mariano, Mathematical Reviews, Issue 2012 j)
