Mathematical Problems in the Theory of Bone Poroelasticity
This paper concerns with the quasi-static theory of bone poroelasticity for materials with double porosity. The system of equations of this theory based on the equilibrium equations, conservation of fluid mass, the effective stress concept and Darcy’s law for material with double porosity. The inter...
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| Format: | Article |
| Language: | English |
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Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2012-12-01
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| Series: | Biomath |
| Subjects: | |
| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/38 |
| _version_ | 1797727630253883392 |
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| author | Merab Svanadze Antonio Scalia |
| author_facet | Merab Svanadze Antonio Scalia |
| author_sort | Merab Svanadze |
| collection | DOAJ |
| description | This paper concerns with the quasi-static theory of bone poroelasticity for materials with double porosity. The system of equations of this theory based on the equilibrium equations, conservation of fluid mass, the effective stress concept and Darcy’s law for material with double porosity. The internal and external basic boundary value problems (BVPs) are formulated and uniqueness of regular (classical) solutions are proved. The single-layer and double-layer potentials are constructed and their basic properties are established. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral method) and the theory of singular integral equations. |
| first_indexed | 2024-03-12T11:02:23Z |
| format | Article |
| id | doaj.art-53a558b9492e4da7973eb8dc2a5b3381 |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T11:02:23Z |
| publishDate | 2012-12-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-53a558b9492e4da7973eb8dc2a5b33812023-09-02T04:31:22ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182012-12-011210.11145/j.biomath.2012.11.22536Mathematical Problems in the Theory of Bone PoroelasticityMerab Svanadze0Antonio ScaliaIlia State UniversityThis paper concerns with the quasi-static theory of bone poroelasticity for materials with double porosity. The system of equations of this theory based on the equilibrium equations, conservation of fluid mass, the effective stress concept and Darcy’s law for material with double porosity. The internal and external basic boundary value problems (BVPs) are formulated and uniqueness of regular (classical) solutions are proved. The single-layer and double-layer potentials are constructed and their basic properties are established. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral method) and the theory of singular integral equations.http://www.biomathforum.org/biomath/index.php/biomath/article/view/38poroelasticitydouble porosityboundary value problems. |
| spellingShingle | Merab Svanadze Antonio Scalia Mathematical Problems in the Theory of Bone Poroelasticity Biomath poroelasticity double porosity boundary value problems. |
| title | Mathematical Problems in the Theory of Bone Poroelasticity |
| title_full | Mathematical Problems in the Theory of Bone Poroelasticity |
| title_fullStr | Mathematical Problems in the Theory of Bone Poroelasticity |
| title_full_unstemmed | Mathematical Problems in the Theory of Bone Poroelasticity |
| title_short | Mathematical Problems in the Theory of Bone Poroelasticity |
| title_sort | mathematical problems in the theory of bone poroelasticity |
| topic | poroelasticity double porosity boundary value problems. |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/38 |
| work_keys_str_mv | AT merabsvanadze mathematicalproblemsinthetheoryofboneporoelasticity AT antonioscalia mathematicalproblemsinthetheoryofboneporoelasticity |