Lagrange multiplier and singular limit of double obstacle problems for Allen-Cahn equation with constraint

We consider an Allen--Cahn equation with a constraint of double obstacle-type. This constraint is a subdifferential of an indicator function on the closed interval, which is a multivalued function. In this paper we study the properties of the Lagrange multiplier to our equation. Also, we consider the singular limit of our system and clarify the limit of the solution and the Lagrange multiplier to our double obstacle problem. Moreover, we give some numerical experiments of our problem by using the Lagrange multiplier

Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems

An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media equation, Hele-Shaw profile, nonlinear diffusion of singular logarithmic type, nonlinear diffusion of Penrose-Fife type, fast diffusion equation and so on. Namely, by setting the suitable potential of the Cahn-Hilliard systems, all of these problems can be obtained as limits of the Cahn-Hilliard related problems. Convergence results and error estimates are proved

Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary

The well-known Cahn-Hilliard equation entails mass conservation if a suitable boundary condition is prescribed. In the case when the equation is also coupled with a dynamic boundary condition, including the Laplace-Beltrami operator on the boundary, the total mass on the inside of the domain and its trace on the boundary should be conserved. The new issue of this paper is the setting of a mass constraint on the boundary. The effect of this additional constraint is the appearance of a Lagrange multiplier; in fact, two Lagrange multipliers arise, one for the bulk, the other for the boundary. The well-posedness of the resulting Cahn-Hilliard system with dynamic boundary condition and mass constraint on the boundary is obtained. The theory of evolution equations governed by subdifferentials is exploited and a complete characterization of the solution is given.Comment: arXiv admin note: text overlap with arXiv:1405.011

ERAL1 is associated with mitochondrial ribosome and elimination of ERAL1 leads to mitochondrial dysfunction and growth retardation

ERAL1, a homologue of Era protein in Escherichia coli, is a member of conserved GTP-binding proteins with RNA-binding activity. Depletion of prokaryotic Era inhibits cell division without affecting chromosome segregation. Previously, we isolated ERAL1 protein as one of proteins which were associated with mitochondrial transcription factor A by using immunoprecipitation. In this study, we analysed the localization and function of ERAL1 in mammalian cells. ERAL1 was localized in mitochondrial matrix and associated with mitoribosomal proteins including the 12S rRNA. siRNA knockdown of ERAL1 decreased mitochondrial translation, caused redistribution of ribosomal small subunits and reduced 12S rRNA. The knockdown of ERAL1 in human HeLa cells elevated mitochondrial superoxide production and slightly decreased mitochondrial membrane potential. The knockdown inhibited the growth of HeLa cells with an accumulation of apoptotic cells. These results suggest that ERAL1 is localized in a small subunit of the mitochondrial ribosome, plays an important role in the small ribosomal constitution, and is also involved in cell viability

Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs

summary:Recently, we established some generalizations of the theory of Lagrange multipliers arising from nonlinear programming in Banach spaces, which enable us to treat not only elliptic problems but also parabolic problems in the same generalized framework. The main objective of the present paper is to discuss a typical time-dependent double obstacle problem as a new application of the above mentioned generalization. Actually, we describe it as a usual parabolic variational inequality and then characterize it as a parabolic inclusion by using the Lagrange multiplier and the nonlinear maximal monotone operator associated with the time differential under time-dependent double obstacles

An Analytical Approach for Facility Location for Truck Platooning-A Case Study of Unmanned Following Truck Platooning System in Japan

Truck platooning involves a small convoy of freight vehicles using electronic coupling as an application in automated driving technology, and it is expected to represent a major solution for improving efficiency in truck transportation in the near future. Recently, there have been several trials regarding truck platooning with major truck manufacturers and logistics companies on public roads in the United States, European countries and Japan. There is a need to locate a facility for the formation of truck platooning to realize the unmanned operation of trucks following in a platoon. In this study, we introduce the current status of truck platooning in Japan and present the optimal location model for truck platooning using the continuous approximation model with a numerical experiment, considering the case in Japan. We derived the optimal locational strategy for the combination of the long-haul ratio and the cost factor of platooning. With parameters estimated for several scenarios for the deployment of truck platooning in Japan, the numerical results show that the optimal locational strategy for a platoon of manned vehicles and a platoon with unmanned following vehicles is the edge of the local region, and that for a platoon of fully automated vehicles is the center of the region