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The latest research articles published by Boundary Value Problems20150116T00:00:00ZHeat transfer in an unsteady MHD flow through an infinite annulus with radiationAn analytical study of a laminar unsteady magnetohydrodynamic flow of a viscous incompressible and electrically conducting Newtonian nonGray optically thin fluid between two infinite concentric vertical cylinders influenced by time dependent periodic pressure gradient subjected to a magnetic field applied in azimuthal direction and in the presence of appreciable thermal radiation and periodic wall temperature is presented. The governing equations of motion and energy are transformed into ordinary differential equations which are solved in closed form in terms of the modified Bessel functions (of first and second kind) of order zero. The induced magnetic field is neglected, assuming the magnetic Reynolds number to be considerably small. A parametric study accounting for the effects of various physical parameters on the velocity and temperature fields and on the coefficient of skin friction, the rate of heat transfer at the surface of the cylinders, and mass flux across a normal section of the annulus is conducted and the results are discussed graphically.MSC: 76W05.
http://www.boundaryvalueproblems.com/content/2015/1/11
Nazibuddin AhmedManas DuttaBoundary Value Problems 2015, null:1120150116T00:00:00Zdoi:10.1186/s136610140279z/content/figures/s136610140279ztoc.gifBoundary Value Problems16872770${item.volume}1120150116T00:00:00ZXMLDecay estimate of solutions for a semilinear wave equationIn this paper, we investigate the initial value problem for a semilinear wave equation in ndimensional space. Under a smallness condition on the initial value, the global existence and decay estimates of the solutions are established. Furthermore, time decay estimates for the spatial derivatives of the solution are provided. The proof is carried out by means of the decay property of the solution operator and a fixed pointcontraction mapping argument.MSC: 35L30, 35L75.
http://www.boundaryvalueproblems.com/content/2015/1/10
Hengjun ZhaoJiya NuenBoundary Value Problems 2015, null:1020150116T00:00:00Zdoi:10.1186/s1366101402726/content/figures/s1366101402726toc.gifBoundary Value Problems16872770${item.volume}1020150116T00:00:00ZXMLClosedform solutions for accelerated MHD flow of a generalized Burgers¿ fluid in a rotating frame and porous mediumClosedform solutions for magnetohydrodynamic (MHD) and rotating flow of generalized Burgers’ fluid past an accelerated plate embedded in a porous medium are obtained using the Laplace transform technique. Modified Darcy’s law for generalized Burgers’ fluid is taken into account. Both constant and variable acceleration cases are considered. The graphical results along with illustrations are presented to bring out the effects of indispensable parameters on the velocity. The obtained solutions are reduced as special cases to their limiting solutions by taking some suitable parameters equal to zero.
http://www.boundaryvalueproblems.com/content/2015/1/8
Ilyas KhanFarhad AliNorzieha MustaphaSharidan ShafieBoundary Value Problems 2015, null:820150115T12:00:00Zdoi:10.1186/s1366101402584/content/figures/s1366101402584toc.gifBoundary Value Problems16872770${item.volume}820150115T12:00:00ZXMLNumerical simulation for twophase flow in a porous mediumIn this paper, we introduce a numerical study of the hydrocarbon system used for petroleum reservoir simulations. This system is a simplified model which describes a twophase flow (oil and gas) with mass transfer in a porous medium, which leads to fluid compressibility. This kind of flow is modeled by a system of parabolic degenerated nonlinear convectiondiffusion equations. Under certain hypotheses, such as the validity of Darcy’s law, incompressibility of the porous medium, compressibility of the fluids, mass transfer between the oil and the gas, and negligible gravity, the global pressure formulation of Chavent (Mathematical Models and Finite Elements for Reservoir Simulation: Single Phase, Multiphase and Multicomponent Flows Through Porous Media, 1986) is formulated. This formulation allows the establishment of theoretical results on the existence and uniqueness of the solution (Gasmi and Nouri in Appl. Math. Sci. 7(42):20552064, 2013). Furthermore, different numerical schemes have been considered by many authors, among others we can refer the reader to (Chen in Finite element methods for the black oil model in petroleum reservoirs, 1994; Chen in Reservoir Simulation: Mathematical Techniques in Oil Recovery, 2007) and (Gagneux et al. in Rev. Mat. Univ. Complut. Madr. 2(1):119148, 1989). Here we make use of a scheme based on the finite volume method and present numerical results for this simplified system.
http://www.boundaryvalueproblems.com/content/2015/1/7
Souad GasmiFatma NouriBoundary Value Problems 2015, null:720150113T12:00:00Zdoi:10.1186/s1366101402566/content/figures/s1366101402566toc.gifBoundary Value Problems16872770${item.volume}720150113T12:00:00ZXMLSpectral analysis of the integral operator arising from the beam deflection problem on elastic foundation II: eigenvaluesWe analyze the eigenstructure of the integral operator
K
l
,
α
,
k
which arise naturally from the beam deflection equation on linear elastic foundation with finite beam. We show that
K
l
,
α
,
k
has countably infinite number of positive eigenvalues approaching 0 as the limit, and give explicit upper and lower bounds on each of them. Consequently, we obtain explicit upper and lower bounds on the
L
2
norm of the operator
K
l
,
α
,
k
. We also present precise approximations of the eigenvalues as they approach the limit 0, which describes the almost regular structure of the spectrum of
K
l
,
α
,
k
. Additionally, we analyze the dependence of the eigenvalues, including the
L
2
norm of
K
l
,
α
,
k
, on the intrinsic length
L
=
2
l
α
of the beam, and show that each eigenvalue is continuous and strictly increasing with respect to L. In particular, we show that the respective limits of each eigenvalue as L goes to 0 and infinity are 0 and
1
/
k
, where k is the linear spring constant of the given elastic foundation. Using Newton’s method, we also compute explicitly numerical values of the eigenvalues, including the
L
2
norm of
K
l
,
α
,
k
, corresponding to various values of L.MSC: 34L15, 47G10, 74K10.
http://www.boundaryvalueproblems.com/content/2015/1/6
Sung ChoiBoundary Value Problems 2015, null:620150113T12:00:00Zdoi:10.1186/s1366101402682/content/figures/s1366101402682toc.gifBoundary Value Problems16872770${item.volume}620150113T12:00:00ZXMLPeriodic solutions for a singular damped differential equationBased on a variational approach, we prove that a secondorder singular damped differential equation has at least one periodic solution when some reasonable assumptions are satisfied.MSC: 34C37, 35A15, 35B38.
http://www.boundaryvalueproblems.com/content/2015/1/5
Jing LiShengjun LiZiheng ZhangBoundary Value Problems 2015, null:520150110T12:00:00Zdoi:10.1186/s1366101402691/content/figures/s1366101402691toc.gifBoundary Value Problems16872770${item.volume}520150110T12:00:00ZXMLA free boundary problem arising in the ecological models with N speciesThis paper is concerned with the onedimensional free boundary problem for quasilinear reactiondiffusion systems arising in the ecological models with Nspecies, where some of the species are made up of two separated groups and the mankind’s influence is taken into account. In the problem under consideration, there are n free boundaries, the coefficients of the equations are allowed to be discontinuous on the free boundaries and the reaction functions are mixed quasimonotone. The aim is to show the local existence of the solutions for the free boundary problem by the fixed point method, and the global existence and uniqueness of the solutions for the corresponding diffraction problem by the approximation and estimate methods.MSC: 35R35, 35R05, 35K57, 35K20.
http://www.boundaryvalueproblems.com/content/2015/1/4
QiJian TanBoundary Value Problems 2015, null:420150110T12:00:00Zdoi:10.1186/s1366101402673/content/figures/s1366101402673toc.gifBoundary Value Problems16872770${item.volume}420150110T12:00:00ZXMLAsymptotic stability of standing waves for the coupled nonlinear Schrödinger systemThis paper considers the asymptotic stability of standing waves of a coupled nonlinear Schrödinger system with an attractive potential. Meanwhile, the existence of a center manifold is obtained.
http://www.boundaryvalueproblems.com/content/2015/1/3
Yang LiaoQuanbao SunXin ZhaoMing ChengBoundary Value Problems 2015, null:320150110T12:00:00Zdoi:10.1186/s1366101402664/content/figures/s1366101402664toc.gifBoundary Value Problems16872770${item.volume}320150110T12:00:00ZXMLTriple positive solutions of fourthorder impulsive differential equations with integral boundary conditionsBy using LeggettWilliams’ fixed point theorem and Hölder’s inequality, the existence of three positive solutions for the fourthorder impulsive differential equations with integral boundary conditions
x
(
4
)
(
t
)
=
ω
(
t
)
f
(
t
,
x
(
t
)
)
,
0
<
t
<
1
,
t
≠
t
k
,
Δ
x

t
=
t
k
=
I
k
(
t
k
,
x
(
t
k
)
)
,
Δ
x
′

t
=
t
k
=
0
,
k
=
1
,
2
,
…
,
m
,
x
(
0
)
=
∫
0
1
g
(
s
)
x
(
s
)
d
s
,
x
′
(
1
)
=
0
,
x
″
(
0
)
=
∫
0
1
h
(
s
)
x
″
(
s
)
d
s
,
x
‴
(
1
)
=
0
is considered, where
ω
(
t
)
is
L
p
integrable. Our results cover a fourthorder boundary value problem without impulsive effects and are compared with some recent results.
http://www.boundaryvalueproblems.com/content/2015/1/2
Yaling ZhouXueMei ZhangBoundary Value Problems 2015, null:220150110T12:00:00Zdoi:10.1186/s1366101402637/content/figures/s1366101402637toc.gifBoundary Value Problems16872770${item.volume}220150110T12:00:00ZXMLExistence and nonexistence of solutions for a generalized Boussinesq equationThe Cauchy problem for a generalized Boussinesq equation is investigated. The existence and uniqueness for the local solution and global solution of the problem are established under certain conditions. Moreover, the potential well method is used to discuss the finitetime blowup for the problem.MSC: 35Q20, 76B15.
http://www.boundaryvalueproblems.com/content/2015/1/1
Ying WangBoundary Value Problems 2015, null:120150110T12:00:00Zdoi:10.1186/s1366101402593/content/figures/s1366101402593toc.gifBoundary Value Problems16872770${item.volume}120150110T12:00:00ZXML