The Analytical Method in Geomechanics

2007 ◽  
Vol 60 (3) ◽  
pp. 87-106 ◽  
Author(s):  
A. P. S. Selvadurai
Keyword(s):  
Porous Media ◽  
Boundary Value Problems ◽  
Analytical Method ◽  
Boundary Value ◽  
Practical Importance ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Flow And Transport ◽  
Initial Boundary Value

This article presents an overview of the application of analytical methods in the theories of elasticity, poroelasticity, flow, and transport in porous media and plasticity to the solution of boundary value problems and initial boundary value problems of interest to geomechanics. The paper demonstrates the role of the analytical method in geomechanics in providing useful results that have practical importance, pedagogic value, and serve as benchmarking tools for calibrating computational methodologies that are ultimately used for solving more complex practical problems in geomechanics. There are 315 references cited in this article.

scholarly journals SOLVABILITY OF HOMOGENIZED PROBLEMS WITH CONVOLUTIONS FOR WEAKLY POROUS MEDIA

2020 ◽  
pp. 59-70
Author(s):  
G. V. Sandrakov ◽  
A. L. Hulianytskyi
Keyword(s):  
Porous Media ◽  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Initial Conditions ◽  
Boundary Value ◽  
A Priori ◽  
Initial Boundary ◽  
Parabolic Problems ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

Initial boundary value problems for nonstationary equations of diffusion and filtration in weakly porous media are considered. Assertions about the solvability of such problems and the corresponding homogenized problems with convolutions are given. These statements are proved for general initial data and inhomogeneous initial conditions and are generalizations of classical results on the solvability of initial-boundary value problems for the heat equation. The proofs use the methods of a priori estimates and the well-known Agranovich–Vishik method, developed to study parabolic problems of general type.

scholarly journals Blowing-up solutions of the time-fractional dispersive equations

2021 ◽  
Vol 10 (1) ◽  
pp. 952-971
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Mokhtar Kirane ◽  
Berikbol T. Torebek
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Nonlinear Capacity ◽  
Blowing Up ◽  
De Vries ◽  
Initial Boundary Value

Abstract This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions for the blowing-up of solutions in finite time of aforementioned equations are presented. We also discuss the maximum principle and influence of gradient non-linearity on the global solvability of initial-boundary value problems for the time-fractional Burgers equation. The main tool of our study is the Pohozhaev nonlinear capacity method. We also provide some illustrative examples.

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