Stability and wave motion in porous media straughan brian
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In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. The first three chapters form a comprehensive survey of most modern contributions also describing in detail the mathematical properties of each model. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. People having already some knowledge of flows in porous media will be delighted to read it, and beginners will find a valuable guide to understanding many challenging problems, treated with mathematical rigour, but never forgetting the physics. Since stability properties inevitably end up requiring to solve a multi-parameter eigenvalue problem by computational means, a separate chapter is devoted to this topic.

Temporal stability studies of a variety of problems are included, indic- ingpracticalapplicationsofeach. The E-mail message field is required. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Brian Straughan is a professor at the Department of Mathematical Sciences at Durham University, United Kingdom. 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. Stability and wave motion in porous media.

A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Thermal convection and stability of other flows in porous media are covered and a chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Throughout, we include several new results not published elsewhere. The first three chapters form a comprehensive survey of most modern contributions also describing in detail the mathematical properties of each model. Thus, this text should be a valuable resource for anybody working on problems in the porous media field.

This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications. 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. In particular, the chapter dealing with this problem contains some new material only p- lished here. A chapter is included on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. 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.

In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. The important mathematical quations about structural stability and spatial decay are address. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Acoustic waves in porous media are also analysed in some detail. 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.

The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. The final two chapters are devoted to a description of selected applications and the corresponding formation of mathematical models. The book, written by well-known experts, addresses researchers and students interested in physical aspects of our environment. Description This book describes several tractable theories for fluid flow in porous media.

The text also presents other relevant improperly posed problems, including the uniqueness and continuous dependence for singular equations, the spatial decay in improperly posed parabolicproblems, the uniqueness for the backward in time Navier-Stokes equations on an unbounded domain, the improperly posed problems for dusty gases, the linear thermoelasticity, and the overcoming Holder continuity and image restoration. Acceleration waves and shock waves are the focus in the next two chapters. Among the topics presented are: classical fluid equations, catastrophic behavior in nonlinear fluid theories, blow-up in Volterra equations, and rapid energy growth in parallel flows. Thermal convection and stability of other flows in porous media are covered and a chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Bothlinearinstabilityanalysisandglobal nonlinear stability thresholds are presented where possible.

Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Thus, this text should be a valuable resource for anybody working on problems in the porous media field. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Among the topics presented are: classical fluid equations, catastrophic behavior in nonlinear fluid theories, blow-up in Volterra equations, and rapid energy growth in parallel flows. Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.

Thermal convection and stability of other flows in porous media are covered. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Such a diverse collection demonstrates that an interdisciplinary approach is essential to modelling tipping points in health and social problems, and the assessment of associated risk and resilience. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion. We believe this is the? The book addresses continuous dependence on initial-time and spatial geometry and on modeling backward and forward in time. The E-mail message field is required.