Mathematical Theories of Nanoporous Media

This book presents a comprehensive framework for the linear theories of elasticity and thermoelasticity of nanoporous materials with quadruple voids, developing models based on pore volume fractions and extending them to rigid bodies with the same structure. Using the potential method and modern singular integral equation theory, it systematically analyzes a broad class of non-classical boundary value problems, including equilibrium, steady vibrations, pseudo-oscillations, quasi-static processes, and heat conduction. Combining original, previously unpublished results, the work significantly advances the mathematical foundations of nanoporous media and offers a unified continuum-mechanical approach with important applications in fields such as engineering, geomechanics, materials science, and biomechanics, particularly for modeling complex biological tissues.