Stabilization and numerical treatment for swelling porous elastic soils with fluid saturation

被引：3

作者：

Almeida Junior, Dilberto S. ^{[1
]}

Ramos, Anderson J. A. ^{[2
]}

Noe, Alberto S. ^{[1
,3
]}

Freitas, Mirelson M. ^{[2
]}

Aum, Pedro T. P. ^{[4
]}

机构：

[1] Fed Univ Para, Program Math, Augusto Correa St 01, BR-66075110 Belem, PA, Brazil

[2] Fed Univ Para, Fac Math, Raimundo Santana St S-N, BR-68721000 Salinopolis, PA, Brazil

[3] Univ Zambeze, Fac Ciencias & Tecnol, Av Alfredo Lawley 1018, Matacuane, Beira Sofala, Mozambique

[4] Fed Univ Para, Fac Petr Engn, Raimundo Santana St S-N, BR-68721000 Salinopolis, PA, Brazil

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2021年 / 101卷 / 11期

关键词：

exponential stability; finite-difference discretization; swelling porous elastic; EXPONENTIAL STABILITY; DEPENDENCE; MIXTURES; UNIQUENESS; BEHAVIOR;

D O I：

10.1002/zamm.202000366

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the current study, we analyze the asymptotic behavior of the solutions of one-dimensional initial boundary value problem associated with the isothermal linear theory of swelling porous elastic media. Our main results are the well-posedness of the system as well as the exponential stabilization of solution and the discretization of the equations using a particular numerical scheme, which allowed us to prove the monotonicity of the discrete energy. In addition, we provide the numerical simulations of the solution and the total energy that explain the results obtained. Our results are achieved by using the semigroup theory and for the results in finite dimensional we used finite differences.

引用

页数：19

共 33 条

[1]

Aksu I., 2015, GeoResJ, V7, P1, DOI 10.1016/j.grj.2015.02.003

[2] Exponential stability in thermoviscoelastic mixtures of solids [J].

Alves, M. S. ;

Munoz Rivera, J. E. ;

Sepulveda, M. ;

Villagran, O. V. .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2009, 46 (24) :4151-4162

[3] Exponential decay in a thermoelastic mixture of solids [J].

Alves, M. S. ;

Munoz Rivera, J. E. ;

Quintanilla, R. .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2009, 46 (7-8) :1659-1666

[4]

Ames B., 1997, Non-standard and improperly posed problems

[5] Energy properties preserving schemes for Burgers' equation [J].

Anguelov, R. ;

Djoko, J. K. ;

Lubuma, J. M. -S. .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2008, 24 (01) :41-59

[6] CONTINUUM THEORIES OF MIXTURES - BASIC THEORY AND HISTORICAL DEVELOPMENT [J].

ATKIN, RJ ;

CRAINE, RE .

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1976, 29 (MAY) :209-244

[7] THEORIES OF IMMISCIBLE AND STRUCTURED MIXTURES [J].

BEDFORD, A ;

DRUMHELLER, DS .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1983, 21 (08) :863-960

[8] Anti-plane shear deformations of swelling porous elastic soils [J].

Bofill, F ;

Quintanilla, R .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2003, 41 (08) :801-816

[9]

Bowen R. M., 1976, CONTINUUM PHYS, VIII, P689

[10] DIFFUSION IN MIXTURES OF ELASTIC MATERIALS [J].

BOWEN, RM ;

WIESE, JC .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1969, 7 (07) :689-&

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