## Journals

- Advances in Mathematics of Communications
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### Open Access Journals

DCDS-S

The behavior of polygonal curves with asymptotic lines to
crystalline motion with the bulk effect is discussed.
We show sufficient conditions for
global existence of the solutions and characterize facet-extinction patterns.
We also show the eventual monotonicity of shape of the solution curves,
that is, the solutions become V-shaped in finite time.

DCDS

The asymptotic behavior of solutions to an anisotropic crystalline motion is investigated.
In this motion,
a solution polygon changes the shape by a power of crystalline curvature in its
normal direction and develops singularity in a finite time.
At the final time,
two types of singularity appear:
one is a single point-extinction and the other is degenerate pinching.
We will discuss the latter case of singularity and show the
exact blow-up rate for a fast blow-up or a type II blow-up
solution which arises in an equivalent blow-up problem.

DCDS-S

In this paper we propose a crystalline motion of spiral-shaped polygonal
curves with a tip motion as a simple model of a step motion on a
crystal surface under screw dislocation. We give a tip motion and
discuss the behavior of the solution curves by crystalline curvature
flow with a driving force. We show that the solution curve belongs
to a suitable class of spiral-shaped curves and also show a time-global
existence of the spiral-shaped solutions.

PROC

In this short paper we propose a finite difference scheme for the
Landau-Lifshitz equation and an iteration procedure to solve the scheme.
The key concept is ``structure-preserving''.
We show that the proposed method inherits important mathematical structures
from the original problem and also analysis the iteration.

DCDS-S

This issue consists of 16 carefully refereed papers dealing with mathematical
modeling, numerical analysis, numerical simulation and mathematical analysis
for ordinary/partial differential equations in several fields: fluid dynamics,
chemistry, crystal physics, material science, medical science and biology.
The authors in the present issue are mainly from Czech Republic, Slovakia and Japan. Scientific and mathematical exchanges began in 2004 among the authors and their friends. Since then, fruitful relationships and effective exchanges have been promoted and developed.
Professor Tatsuyuki Nakaki strongly supported these exchanges and established the Czech-Slovak-Japanese joint seminars on industrial and applied mathematics.
Unfortunately, he passed away in 2011.
In 2013 in Tokyo, we had an opportunity to have a meeting in honor of Professor Nakaki.
Recent topics in industrial and applied mathematics were widely discussed and
we could exchange new ideas and various kinds of new problems.
The present issue includes a part of those results.

Finally we would like to thank the referees for their valuable comments in reviewing the papers.

Finally we would like to thank the referees for their valuable comments in reviewing the papers.

keywords:

PROC

This paper deals with behavior of polygonal plane curves with two
asymptotic lines by generalized crystalline curvature flow with a driving force.
We show global existence of V-shaped solutions and investigate the deformation
patterns of non-V-shaped solutions. We also show that non-V-shaped solutions
become V-shaped in finite time.

DCDS-S

In our previous paper we proposed a crystalline motion of spiral-shaped polygonal
curves with a tip motion as a simple model of a step motion on a
crystal surface under screw dislocation and discussed global existence
of spiral solutions to the proposed model.
In this paper we extend the previous results for generalized crystalline curvature
flow with a suitable tip motion.
We show that solution curves never intersect a trajectory of a tip
and has no self-intersections. We also show that any facet never
disappear during time evolution.
Finally we show a time-global existence of the spiral-shaped solutions.

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