| 1. |
- Aiki, Toyohiko, et al.
(författare)
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A free boundary problem describing migration into rubbers : Quest of the large time behavior
- 2022
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Ingår i: Zeitschrift für angewandte Mathematik und Mechanik. - : John Wiley & Sons. - 0044-2267 .- 1521-4001. ; 102:7
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Tidskriftsartikel (refereegranskat)abstract
- In many industrial applications, rubber-based materials are routinely used in conjunction with various penetrants or diluents in gaseous or liquid form. It is of interest to estimate theoretically the penetration depth as well as the amount of diffusants stored inside the material. In this framework, we prove the global solvability and explore the large time-behavior of solutions to a one-phase free boundary problem with nonlinear kinetic condition that is able to describe the migration of diffusants into rubber. The key idea in the proof of the large time behavior is to benefit from a contradiction argument, since it is difficult to obtain uniform estimates for the growth rate of the free boundary due to the use of a Robin boundary condition posed at the fixed boundary.
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| 2. |
- Aiki, Toyohiko, et al.
(författare)
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A macro-micro elasticity-diffusion system modeling absorption-induced swelling in rubber foams : Proof of the strong solvability
- 2021
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Ingår i: Quarterly of Applied Mathematics. - : American Mathematical Society (AMS). - 0033-569X .- 1552-4485. ; 79:3, s. 545-579
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we propose a macro-micro (two-scale) mathematical model for describing the macroscopic swelling of a rubber foam caused by the microscopic absorption of some liquid. In our modeling approach, we suppose that the material occupies a one-dimensional domain which swells as described by the standard beam equation including an additional term determined by the liquid pressure. As special feature of our model, the absorption takes place inside the rubber foam via a lower length scale, which is assumed to be inherently present in such a structured material. The liquid's absorption and transport inside the material is modeled by means of a nonlinear parabolic equation derived from Darcy's law posed in a non-cylindrical domain defined by the macroscopic deformation (which is a solution of the beam equation). Under suitable assumptions, we establish the existence and uniqueness of a suitable class of solutions to our evolution system coupling the nonlinear parabolic equation posed on the microscopic non-cylindrical domain with the beam equation posed on the macroscopic cylindrical domain. In order to guarantee the regularity of the non-cylindrical domain, we impose a singularity to the elastic response function appearing in the beam equation.
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| 3. |
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| 4. |
- Aiki, Toyohiko, et al.
(författare)
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Differentiability of a solution of a free boundary problem describing water adsorption
- 2020
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Ingår i: Advances in Mathematical Sciences and Applications. - : GAKKO TOSHO CO. - 1343-4373. ; 29, s. 247-282
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Tidskriftsartikel (refereegranskat)abstract
- Sato-Aiki-Murase-Shirakawa [7, 16] proposed a free boundary problem in order to describe water adsorption appearing in moisture transport of concrete carbonation process. The problem is to find a pair of a curve and a function for given boundary and initial functions. In this paper we consider that the boundary and initial functions depend on some parameter. Kumazaki [9, 10] already proved the continuous and measurable properties of solutions with respect to the parameter. The aim of this paper is to establish differentiability of solutions with respect to the parameter as a new property. This result will be applied to research of the multi-scale model to water adsorption in concrete carbonation.
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| 5. |
- Aiki, Toyohiko, et al.
(författare)
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Existence and Uniqueness of Weak Solutions for the Model Representing Motions of Curves Made of Elastic Materials
- 2021
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Ingår i: Bulletin of Irkutsk State University, Series Mathematics. - : Irkutsk State University. - 1997-7670 .- 2541-8785. ; 36, s. 44-56
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Tidskriftsartikel (refereegranskat)abstract
- We consider the initial boundary value problem for the beam equation with the nonlinear strain. In our previous work this problem was proposed as a mathematical model for stretching and shrinking motions of the curve made of the elastic material on the plane. The aim of this paper is to establish uniqueness and existence of weak solutions. In particular, the uniqueness is proved by applying the approximate dual equation method.
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| 6. |
- Aiki, Toyohiko, et al.
(författare)
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Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data
- 2013
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Ingår i: Nonlinear Analysis. - : Elsevier. - 0362-546X .- 1873-5215. ; 93, s. 3-14
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Tidskriftsartikel (refereegranskat)abstract
- We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the t-behavior of reaction penetration depths by including nonlinear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data.
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| 8. |
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| 9. |
- Aiki, Toyohiko, et al.
(författare)
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Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions
- 2017
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Ingår i: Journal of Differential Equations. - : Elsevier. - 0022-0396 .- 1090-2732. ; 5:5, s. 3009-3026
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Tidskriftsartikel (refereegranskat)abstract
- We prove the large time behavior of solutions to a coupled thermo-diffusion arising in the modeling of the motion of hot colloidal particles in porous media. Additionally, we also ensure the uniqueness of solutions of the target problem. The main mathematical difficulty is due to the presence in the right-hand side of the equations of products between temperature and concentration gradients. Such terms mimic the so-called thermodynamic Soret and Dufour effects. These are cross-coupling terms emphasizing in this context a strong interplay between heat conduction and molecular diffusion.
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