Colli P.,University of Pavia |
Fukao T.,Kyoto University of Education
Mathematical Methods in the Applied Sciences | Year: 2015
The Allen-Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint, which may involve either the solution inside the domain or its trace on the boundary. The system of nonlinear partial differential equations can be formulated as a variational inequality. The presence of the constraint in the evolution process leads to additional terms in the equation and the boundary condition containing a suitable Lagrange multiplier. A well-posedness result is proved for the related initial value problem. © 2014 John Wiley & Sons, Ltd.
Kiriki S.,Kyoto University of Education |
Soma T.,Tokyo Metroplitan University
Nonlinearity | Year: 2012
In this paper, we give sufficient conditions for the existence of C 2 robust heterodimensional tangency, and present a non-empty open set in Diff 2(M) with dim M3 each element of which has a non-degenerate heterodimensional tangency on a C 2 robust heterodimensional cycle. © 2012 IOP Publishing Ltd & London Mathematical Society.
Bonatti C.,Institute Of Mathematiques Of Bourgogne |
Diaz L.J.,Pontifical Catholic University of Rio de Janeiro |
Kiriki S.,Kyoto University of Education
Nonlinearity | Year: 2012
We consider diffeomorphisms f with heteroclinic cycles associated with saddles P and Q of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to f with a robust cycle associated with hyperbolic sets containing the continuations of P and Q. We focus on the case where the indices of these two saddles differ by one. We prove that, excluding one particular case (so-called twisted cycles that additionally satisfy some geometrical restrictions), all such cycles can be stabilized. © 2012 IOP Publishing Ltd & London Mathematical Society.
Yokoyama T.,Kyoto University of Education
Journal of Dynamical and Control Systems | Year: 2015
Consider the set (Formula presented.) of non-wandering continuous flows on a closed surface M. Then we show that such a flow can be approximated by a non-wandering flow v such that the complement M−Per(v) of the set of periodic points is the union of finitely many centers and finitely many homoclinic saddle connections. Using the approximation, the following are equivalent for a continuous non-wandering flow v on a closed connected surface M: (1) the non-wandering flow v is topologically stable in (Formula presented.); (2) the orbit space M/v is homeomorphic to a closed interval; (3) the closed connected surface M is not homeomorphic to a torus but consists of periodic orbits and at most two centers. Moreover, we show that a closed connected surface has a topologically stable continuous non-wandering flow in (Formula presented.) if and only if the surface is homeomorphic to either the sphere (Formula presented.), the projective plane (Formula presented.), or the Klein bottle (Formula presented.). © 2015 Springer Science+Business Media New York
Marunaka Y.,Kyoto Prefectural University of Medicine |
Marunaka Y.,Kyoto University of Education
Journal of Pharmacological Sciences | Year: 2014
Epithelial Na+ transport participates in control of various body functions and conditions: e.g., homeostasis of body fluid content influencing blood pressure, control of amounts of fluids covering the apical surface of alveolar epithelial cells at appropriate levels for normal gas exchange, and prevention of bacterial/viral infection. Epithelial Na+ transport via the transcellular pathway is mediated by the entry step of Na+ across the apical membrane via Epithelial Na+ Channel (ENaC) located at the apical membrane, and the extrusion step of Na+ across the basolateral membrane via the Na+,K+-ATPase located at the basolateral membrane. The rate-limiting step of the epithelial Na+ transport via the transcellular pathway is generally recognized to be the entry step of Na+ across the apical membrane via ENaC. Thus, up-/down-regulation of ENaC essentially participates in regulatory systems of blood pressure and normal gas exchange. Amount of ENaC-mediated Na+ transport is determined by the number of ENaCs located at the apical membrane, activity (open probability) of individual ENaC located at the apical membrane, single channel conductance of ENaC located at the apical membrane, and driving force for the Na+ entry via ENaCs across the apical membrane. In the present review article, I discuss the characteristics of ENaC and how these factors are regulated. © The Japanese Pharmacological Society.