Potential Method in Mathematical Theories of Multi-Porosity Media

Beschreibung

This monograph explores the application of the potential method to three-dimensional problems of the mathematical theories of elasticity and thermoelasticity for multi-porosity materials.  These models offer several new possibilities for the study of important problems in engineering and mechanics involving multi-porosity materials, including geological materials (e.g., oil, gas, and geothermal reservoirs); manufactured porous materials (e.g., ceramics and pressed powders); and biomaterials (e.g., bone and the human brain).  
Proceeding from basic to more advanced material, the first part of the book begins with fundamental solutions in elasticity, followed by Galerkin-type solutions and Green’s formulae in elasticity and problems of steady vibrations, quasi-static, and pseudo-oscillations for multi-porosity materials.  The next part follows a similar format for thermoelasticity, concluding with a chapter on problems of heat conduction for rigid bodies. The final chapter then presents a number of open research problems to which the results presented here can be applied. All results discussed by the author have not been published previously and offer new insights into these models.
Potential Method in Mathematical Theories of Multi-Porosity Media will be a valuable resource for applied mathematicians, mechanical, civil, and aerospace engineers, and researchers studying continuum mechanics. Readers should be knowledgeable in classical theories of elasticity and thermoelasticity.
This monograph explores the application of the potential method to three-dimensional problems of the mathematical theories of elasticity and thermoelasticity for multi-porosity materials.  These models offer several new possibilities for the study of important problems in engineering and mechanics involving multi-porosity materials, including geological materials (e.g., oil, gas, and geothermal reservoirs); manufactured porous materials (e.g., ceramics and pressed powders); and biomaterials (e.g., bone and the human brain).  
Proceeding from basic to more advanced material, the first part of the book begins with fundamental solutions in elasticity, followed by Galerkin-type solutions and Green’s formulae in elasticity and problems of steady vibrations, quasi-static, and pseudo-oscillations for multi-porosity materials.  The next part follows a similar format for thermoelasticity, concluding with a chapter on problems of heat conductionfor rigid bodies. The final chapter then presents a number of open research problems to which the results presented here can be applied. All results discussed by the author have not been published previously and offer new insights into these models.
Potential Method in Mathematical Theories of Multi-Porosity Media will be a valuable resource for applied mathematicians, mechanical, civil, and aerospace engineers, and researchers studying continuum mechanics. Readers should be knowledgeable in classical theories of elasticity and thermoelasticity.
Applies the potential method to non-classical three-dimensional problems of the modern mathematical theories of elasticity and thermoelasticity for quadruple porosity materials Suggests future areas of research by presenting readers with numerous perspectives to explore after they have finished Provides a self-contained overview of theory and research, addressing a wide audience of mathematicians, physicists, engineers, and researchers from a variety of fields

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Merab Svanadze

Themen in »Potential Method in Mathematical Theories of Multi-Porosity Media«

Potential method book Potential method elasticity Porosity math Porosity materials Boundary Value Problems Multi-Porosity Media Galerkin-type solutions Laplace transform space Quadruple porosity materials Thermoelastic stress analysis Thermoelasticity theory Singular integral equation Potential Method Elasticity Mathematics and Solid Mechanics

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“This monograph is a valuable contribution to mathematical physics.” (Vladimir Mityushev, zbMATH 1481.74007, 2022)
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