Mathematical Aspects of Multi-Porosity Continua

This book is devoted to describing theories for porous media where such pores havean inbuilt macro structure and a micro structure. For example, a double porositymaterial has pores on a macro scale, but additionally there are cracks or fissures inthe solid skeleton. The actual body is allowed to deform and thus the underlyingtheory is one of elasticity. Various different descriptions are reviewed. Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentratingon uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9the emphasis is on wave motion in double porosity materials with special attentionpaid to nonlinear waves.The final chapter embraces a novel area where an elastic body with a doubleporosity structure is analyzed, but the thermodynamics allows for heat to travel as awave rather than simply by diffusion. 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.