On the linear problem of swelling porous elastic soils

Quintanilla, R.

doi:10.1016/s0022-247x(02)00003-3

Cited by 21 publications

(4 citation statements)

References 16 publications

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“…If we take 𝜇 𝑧 = 0 and (𝑎 1 + 𝑎 2 )∕𝜌 𝑧 = (𝑎 2 + 𝜇)∕𝜌 𝑢 , we may select initial conditions such that 𝑧 0 = 𝑢 0 and 𝑧 1 = 𝑢 1 and, in this case, the solutions are 𝑧 = 𝑢 and correspond to the solutions of the wave equation. Other problems related to the swelling of porous elastic soils can be found in the following references [18][19][20]. In [21], Wang and Guo considered a problem of swelling of the one-dimensional porous elastic soils with a damping in the equation of the displacement of the fluid and proved that the system is exponentially stable using the spectral method.…”

Section: F I G U R E 1 Clay Swelling Processmentioning

confidence: 99%

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

et al. 2021

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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 wellposedness 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.

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Section: F I G U R E 1 Clay Swelling Processmentioning

confidence: 99%

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

et al. 2021

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“…In this way, a precise model, capable of predicting the swelling of clays, will be of great use in engineering and soil science. Based on the important work of Eringen [29], many authors [30][31][32][33][34] studied the behavior of problems related to soil swelling. For example, Quintanilla considered the one-dimensional system in the linear isothermal theory of swelling porous elastic soils given by…”

Section: Introductionmentioning

confidence: 99%

Stabilization of swelling porous elastic soils with fluid saturation, time varying-delay and time-varying weights

Nonato

Ramos

Raposo

et al. 2021

Z. Angew. Math. Phys.

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In this article we study the well-posedness and exponential stability to the one-dimensional system in the linear isothermal theory of swelling porous elastic soils subject with time-varying weights and time-varying delay. We prove existence of global solution for the problems combining semigroup theory with the Kato's variable norm technique. To prove exponential stability, we apply the energy method without the equal wave speeds assumption.

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“…For the classical theory of a mixture consisting of three components: an elastic solid, a viscous fluid and a gas, some results concerning uniqueness and continuous dependence have been studied by Gale¸s [24], in the isothermal approach, and by Chiri¸tȃ [25] and Quintanilla [26,27], in the general context with thermal effects. We outline that the uniqueness and continuous dependence of solution to the incompressible micropolar flows have been studied by Chiri¸tȃ [28] and Łukaszewicz [29] and the uniqueness results in the theory of microstretch fluids have been established by Ie¸san [30].…”

Section: Introductionmentioning

confidence: 99%

Some uniqueness and stability results in the theory of micropolar solid–fluid mixture

Ghiba

2009

Journal of Mathematical Analysis and Applications

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This paper is devoted to the study of a binary homogeneous mixture of an isotropic micropolar linear elastic solid with an incompressible micropolar viscous fluid. Assuming that the internal energy of the solid and the dissipation energy are positive definite forms, some uniqueness and continuous data dependence results are presented. Also, some estimates which describe the time behaviour of solution are established, provided the above two energies are positive definite forms. These estimates are used to prove that for the linearized equations, in the absence of body loads and for null boundary conditions, the solution is asymptotically stable. Then a uniqueness result under mild assumptions on the constitutive constants is given using the Lagrange-Brun identities method. These mathematical results prove that the approach of a micropolar solid-fluid mixture is in agreement with physical expectations.

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On the linear problem of swelling porous elastic soils

Cited by 21 publications

References 16 publications

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

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

Stabilization of swelling porous elastic soils with fluid saturation, time varying-delay and time-varying weights

Some uniqueness and stability results in the theory of micropolar solid–fluid mixture

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