Applied Mathematical Sciences

3 primary works

The Energy Method, Stability and Nonlinear Convection

by Brian Straughan

Published December 1991

This book is primarily a presentation of nonlinear energy stability obtained in convection problems by means of an integral inequality technique that is referred to as the energy method. While its use was originally based on the kinetic energy of the fluid motion, subsequent work has introduced variations of the classical energy. The new functionals have much in common with the Lyapunov method in partial differential equations and standard terminology in the literature would now appear to be generalized energy methods. In this book, the author describes many of the new generalizations and explains why such a generalization was deemed necessary. Additionally, he explains the physical relevance of the problem and indicates the usefulness of an energy technique in this context.

Stability and Wave Motion in Porous Media

by Brian Straughan

Published 1 January 2008

This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer.

Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail.

A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media.

Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.

Heat Waves

by Brian Straughan

Published 1 January 2011

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.