Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems.
Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenctio...
This book deals with blow-up of a solution to a system of PDEs that arise in practical situations. It begins with a relatively simple account of blow-up in systems of interaction-diffusion equations, then concentrates on mechanics. In particular it deals with the Euler equations, Navier--Stokes equations, models for glacier physics, Korteweg--de-Vries equations, and ferro-hydrodynamics. Blow-up is treated in Volterra equations, stressing how these equations arise in mechanics, e.g. in combustion theory. Further topics are chemotaxis in mathematical biology, change of type, from hyperbolic to...
This book deals with blow-up of a solution to a system of PDEs that arise in practical situations. It begins with a relatively simple account of blow-...
This book presents an account of theories of ?ow in porous media which have proved tractable to analysis and computation. In particular, the t- ories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail. In addition, we study the theory of voids in an elastic material due to J. Nunziato and S. Cowin. The range of validity of each theory is outlined and the mathematical properties are considered. The questions of structural stability, where the stability of the model itself is under cons- eration, and spatial stability are investigated. We believe this is the ?rst such...
This book presents an account of theories of ?ow in porous media which have proved tractable to analysis and computation. In particular, the t- ories ...
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...
This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations. The first three chapters form a...
This book presents an account of theories of ?ow in porous media which have proved tractable to analysis and computation. In particular, the t- ories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail. In addition, we study the theory of voids in an elastic material due to J. Nunziato and S. Cowin. The range of validity of each theory is outlined and the mathematical properties are considered. The questions of structural stability, where the stability of the model itself is under cons- eration, and spatial stability are investigated. We believe this is the ?rst such...
This book presents an account of theories of ?ow in porous media which have proved tractable to analysis and computation. In particular, the t- ories ...
This book is dedicated to Professor Kolumban Hutter of the Darmstadt Univer sity of Technology on the occasion of his 60th birthday on 22 January 200l. Professor Hutter graduated in Civil Engineering from the ETH Zurich, and then worked in industry-related consulting at the Institute of Mechanics and the Laboratory of Hydraulics and Soil Mechanics at the ETH, before embark ing on a PhD in Theoretical and Applied Mechanics in Cornell University. He duly completed his PhD under the supervision of Professor Y. H. Pao, working in the field of the electrodynamics of continuous media. After his...
This book is dedicated to Professor Kolumban Hutter of the Darmstadt Univer sity of Technology on the occasion of his 60th birthday on 22 January 200l...
This book is a revised edition of my earlier book of the same title. The cur- rent edition adopts the structure of the earlier version but is much changed. The introduction now contains definitions of stability. Chapters 2 to 4 ex- plain stability and the energy method in more depth and new sections dealing with porous media are provided. Chapters 5 to 13 are revisions of those in the earlier edition. However, chapters 6 to 12 are substantially revised, brought completely up to date, and have much new material in. Throughout the book new results are provided which are not available elsewhere....
This book is a revised edition of my earlier book of the same title. The cur- rent edition adopts the structure of the earlier version but is much cha...
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...
This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations. The first three chapters form a...
The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial differential equation has been an area of intense re search activity in mathematics. Some ofthe early techniques and results were discussed in the monograph by Payne (1975) and in my earlier monograph, Straughan (1982). Relatively recent accounts of blow-up work in partial dif ferential equations may be found in the review by Levine (1990) and in the book by Samarskii et al. (1994). It is becoming increasingly clear that very rapid instabilities and, indeed, finite time blow-up are being...
The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial differential equation has been an area of intense r...
This book is one of the first devoted to an account of theories of thermal convection which involve local thermal non-equilibrium effects, including a concentration on microfluidic effects. The text introduces convection with local thermal non-equilibrium effects in extraordinary detail, making it easy for readers newer to the subject area to understand. This book is unique in the fact that it addresses a large number of convection theories and provides many new results which are not available elsewhere. This book will be useful to researchers from engineering, fluid mechanics, and applied...
This book is one of the first devoted to an account of theories of thermal convection which involve local thermal non-equilibrium effects, including a...
