Generalized mathematical model of the dynamics of consolidation processes with relaxation

“…Bi-parabolic equations are frequently used to demonstrate different evolutionary processes in natural sciences, especially describe the unique highlights of the elements of deformed water-saturated porous environments during their filtration fusion the load applied [1]- [3]. For physical motivation and other models, the interested reader is referred to [5]- [8,24,25] for more details.…”

Section: Introductionmentioning

confidence: 99%

Modified Quasi Boundary Value method for inverse source biparabolic

Phương

Luc

Long

2020

Advances in the Theory of Nonlinear Analysis and Its Application

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In this study, we study an inverse source problem of the bi-parabolic equation. The problem is severely non-well-posed in the sense of Hadamard, the problem is called well-posed if it satisfies three conditions, such as the existence, the uniqueness, and the stability of the solution. If one of the these properties is not satisfied, the problem is called is non well-posed (ill-posed). According to our research experience, the stability properties of the sought solution are most often violated. Therefore, a regularization method is required. Here, we apply a Modified Quasi Boundary Method to deal with the inverse source problem. Base on this method, we give a regularized solution and we show that the regularized solution satisfies the conditions of the well-posed problem in the sense of Hadarmad. In addition, we present the estimation between the regularized solution and the sought solution by using a priori regularization parameter choice rule.

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“…In practice, such sewage ponds are often filled with concentrated salt solutions, which made it necessary to search and develop efficient techniques for the mathematical modeling of the dynamics of consolidation processes, taking into account salt transfer and some other factors [2][3][4]. Such factors include relaxation phenomena accompanying some filtration processes in deformable media and are due to various reasons [2] such as the necessity of accounting for the complex microstructure of solutions and pore space [6][7][8]. In the studies known to date (see, e.g., [1][2][3][4][5][6][7][8]) the dynamics of consolidation processes in deformable media saturated with salt solutions was simulated using the classical porous medium as a mathematical model [9].…”

Section: Introductionmentioning

confidence: 99%

“…Such factors include relaxation phenomena accompanying some filtration processes in deformable media and are due to various reasons [2] such as the necessity of accounting for the complex microstructure of solutions and pore space [6][7][8]. In the studies known to date (see, e.g., [1][2][3][4][5][6][7][8]) the dynamics of consolidation processes in deformable media saturated with salt solutions was simulated using the classical porous medium as a mathematical model [9]. We will develop a mathematical model to describe the dynamics of the consolidation of process of a porous fractured [10] medium saturated with a salt solution in view of interphase mass exchange, which makes it possible to model the dynamics of this process in, for example, artificially fractured (mine burst, explosions) rock.…”

Section: Introductionmentioning

confidence: 99%