ISSN 19371632(print)
ISSN 19371179(online) 
Current volume

Journal archive


DCDSS is indexed by Science Citation Index Expanded, ISI Alerting Services and Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES).
Each issue is devoted to a specific area of the mathematical, physical and engineering sciences. This area will define a research frontier that is advancing rapidly, often bridging mathematics and sciences. DCDSS is essential reading for mathematicians, physicists, engineers and other physical scientists. The journal is published bimonthly.
DCDSS publishes only Theme Issues: issues with a coherent topic proposed by guest editors. Click here to learn how to submit a theme issue proposal. Occasionally, proposals of an important current topic that is also the main theme of a high quality workshop/meeting are also considered, however, the same rigorous editorial process is applied.
Archived in Portico and CLOCKSS 
TOP 10 Most Read Articles in DCDSS, January 2017
1 
A framework for the development of implicit solvers for incompressible flow problems
Volume 5, Number 6, Pages: 1195  1221, 2012
David J. Silvester,
Alex Bespalov
and Catherine E. Powell
Abstract
References
Full Text
Related Articles
This survey paper reviews some recent developments in the design of
robust solution methods for the NavierStokes equations
modelling incompressible fluid flow. There are two
building blocks in our solution strategy. First, an implicit time integrator that uses
a stabilized trapezoid rule with an explicit
AdamsBashforth method for error control, and second, a
robust Krylov subspace solver for the spatially discretized system.
Numerical experiments are presented that illustrate the effectiveness
of our generic approach. It is further shown that the basic solution strategy can be
readily extended to more complicated models, including
unsteady flow problems with coupled physics and steady flow problems that
are nondeterministic in the sense that they have uncertain input data.

2 
Annihilation of two interfaces in a hybrid system
Volume 8, Number 5, Pages: 857  869, 2015
ShinIchiro Ei,
Kei Nishi,
Yasumasa Nishiura
and Takashi Teramoto
Abstract
References
Full Text
Related Articles
We consider the mixed ODEPDE system called a hybrid system,
in which the two interfaces interact with each other through a
continuous medium and their equations of motion are derived
in a weak interaction framework.
We study the bifurcation property of the resulting hybrid system
and construct an unstable standing pulse solution, which plays
the role of a separator
for dynamic transition from standing breather to annihilation behavior
between two interfaces.

3 
Dynamics of two phytoplankton species
competing for light and nutrient with internal storage
Volume 7, Number 6, Pages: 1259  1285, 2014
SzeBi Hsu
and ChiuJu Lin
Abstract
References
Full Text
Related Articles
We analyze a competition model of two phytoplankton species for a
single nutrient with internal storage and light in a well mixed
aquatic environment. We apply the theory of monotone dynamical
system to determine the outcomes of competition: extinction of two
species, competitive exclusion, stable coexistence and bistability
of two species. We also present the graphical presentation to
classify the competition outcomes and to compare outcome of models with
and without internal storage.

4 
Positivity for the Navier bilaplace, an antieigenvalue and an expected lifetime
Volume 7, Number 4, Pages: 839  855, 2014
Guido Sweers
Abstract
References
Full Text
Related Articles
We address the question, for which $\lambda \in \mathbb{R}$ is the boundary
value problem
\begin{equation*}
\left\{
\begin{array}{cc}
\Delta ^{2}u+\lambda u=f & \text{in }\Omega , \\
u=\Delta u=0 & \text{on }\partial \Omega ,
\end{array}
\right.
\end{equation*}
positivity preserving, that is, $f\geq 0$ implies $u\geq 0$. Moreover, we consider what
happens, when $\lambda $ passes the maximal value for which positivity is
preserved.

5 
Birth of canard cycles
Volume 2, Number 4, Pages: 723  781, 2009
Freddy Dumortier
and Robert Roussarie
Abstract
Full Text
Related Articles
In this paper we consider singular perturbation problems occuring in planar slowfast systems $(\dot x=yF(x,\lambda),\dot y=\varepsilon G(x,\lambda))$ where $F$ and $G$ are smooth or even real analytic for some results, $\lambda$ is a multiparameter and $\varepsilon$ is a small parameter. We deal with turning points that are limiting situations of (generalized) Hopf bifurcations and that we call slowfast Hopf points. We investigate the number of limit cycles that can appear near a slowfast Hopf point and this under very general conditions. One of the results states that for any analytic family of planar systems, depending on a finite number of parameters, there is a finite upperbound for the number of limit cycles that can bifurcate from a slowfast Hopf point.
The most difficult problem to deal with concerns the uniform treatment of the evolution that a limit cycle undergoes when it grows from a small limit cycle near the singular point to a canard cycle of detectable size. This explains the title of the paper. The treatment is based on blowup, good normal forms and appropriate Chebyshev systems. In the paper we also relate the slowdivergence integral as it is used in singular perturbation theory to Abelian integrals that have to be used in studying limit cycles close to the singular point.

6 
On the motion of incompressible inhomogeneous EulerKorteweg
fluids
Volume 3, Number 3, Pages: 497  515, 2010
Miroslav Bulíček,
Eduard Feireisl,
Josef Málek
and Roman Shvydkoy
Abstract
Full Text
Related Articles
We study a system of equations governing evolution of incompressible inhomogeneous EulerKorteweg fluids that describe a class of incompressible elastic materials. A local wellposedness theory is developed on a bounded smooth domain with noslip boundary condition on velocity and vanishing gradient of density. The cases of open space and periodic box are also considered, where the local existence and uniqueness of solutions is shown in Sobolev spaces up to the critical smoothness $\frac{n}{2}+1$.

7 
A LotkaVolterra system with patch structure (related to a multigroup SI epidemic model)
Volume 8, Number 5, Pages: 999  1008, 2015
Yoshiaki Muroya
Abstract
References
Full Text
Related Articles
In this paper, for a LotkaVolterra system with infinite delays and patch structure related to a multigroup SI epidemic model, applying Lyapunov functional techniques without using the form of diagonal dominance of the instantaneous negative terms over the infinite delay terms, we establish the complete global dynamics by a threshold parameter $s(M(0))$, that is, the trivial equilibrium is globally asymptotically stable if $s(M(0)) \leq 0$ and the positive equilibrium is globally asymptotically stable if $s(M(0))>0$, respectively. This offer new type condition of global stability for LotkaVolterra systems with patch structure.

8 
Stationary solutions for some shadow system of the KellerSegel model with logistic growth
Volume 8, Number 5, Pages: 1023  1034, 2015
Tohru Tsujikawa,
Kousuke Kuto,
Yasuhito Miyamoto
and Hirofumi Izuhara
Abstract
References
Full Text
Related Articles
From a viewpoint of the pattern formation, the KellerSegel system with the growth term is studied. This model exhibited various static and dynamic patterns caused by the combination of three effects, chemotaxis, diffusion and growth. In a special case when chemotaxis effect is very strong, some numerical experiment in [1],[22] showed static and chaotic patterns. In this paper we consider the logistic source for the growth and a shadow system in the limiting case that a diffusion coefficient and chemotactic intensity grow to infinity. We obtain the global structure of stationary solutions of the shadow system in the onedimensional case. Our proof is based on the bifurcation, singular perturbation and a level set analysis. Moreover, we show some numerical results on the global bifurcation branch of solutions by using AUTO package.

9 
Behavior of radially symmetric solutions for a free boundary problem
related to cell motility
Volume 8, Number 5, Pages: 989  997, 2015
Harunori Monobe
Abstract
References
Full Text
Related Articles
We consider a free boundary problem related to cell motility.
In the previous work, the author [5] replaced
the boundary condition, in the original problem, with a simple boundary condition
and studied the behavior of radially symmetric solutions for the modified problem.
In this paper, we consider the original mathematical model
and show that the behavior of solutions for the model
is similar to the one of solutions for the modified model
under the certain condition.

10 
Numerical simulation of flow in fluidized beds
Volume 8, Number 5, Pages: 833  846, 2015
Petr Bauer,
Michal Beneš,
Radek Fučík,
Hung Hoang Dieu,
Vladimír Klement,
Radek Máca,
Jan Mach,
Tomáš Oberhuber,
Pavel Strachota,
Vítězslav Žabka
and Vladimír Havlena
Abstract
References
Full Text
Related Articles
The article provides a brief overview of a onedimensional model of twophase flow in the geometry of a circulating fluidized bed combustor exhibiting vertical variability of crosssection.
The model is based on numerical solution of conservation laws for mass, momentum and energy
of gas and solid components of the fluidizedbed system by means of the finitevolume method in space and of a multistep higherorder solver in time.
The presented computational results reproduce characteristic behavior of fluidized beds in the given geometry.

Go to top

