Explicit Solutions of the Boundary Value Problems for an Ellipse with Double Porosity

Abstract

The basic two-dimensional boundary value problems of the fully coupled linear equilibrium theory of elasticity for solids with double porosity structure are reduced to the solvability of two types of a problem. The first one is the BVPs for the equations of classical elasticity of isotropic bodies, and the other is the BVPs for the equations of pore and fissure fluid pressures. The solutions of these equations are presented by means of elementary (harmonic, metaharmonic, and biharmonic) functions. On the basis of the gained results, we constructed an explicit solution of some basic BVPs for an ellipse in the form of absolutely uniformly convergent series.

Thermodynamics of Irreversible Processes: Fundamental Constraints, Representations, and Formulation of Boundary Conditions

“…Fortunately, Equation ( 4) is ensured by the extremum principle for the parabolic diffusion equation [63], provided that c(x, t = 0) = c 0 (x) ≥ 0. However, in dealing with more complex transport equations, in which the expression for the fluxes has been obtained from continuous thermodynamic theories, the fulfillment of the positivity constraint is far from being guaranteed.…”

Boundary Value Problems of Thermoelasticity for Porous Sphere and for A Space with Spherical Cavity

“…For applications, it is especially important to construct the solutions of BVPs in explicit form because such solutions enable us to effectively perform quantitative analysis of the investigated problems. Questions related to this topic, different types of problems in the theory of elasticity and thermoelasticity of porous materials are considered, for example, in the works [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], where the explicit solutions are constructed for some BVPs for the concrete domains.…”

Explicit solutions of the BVPs of the theory of thermoelasticity for an elastic circle with voids and microtemperatures

“…Many problems are investigated for elastic materials with microstructures by several researchers (see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and references given there).…”