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The latest research articles published by Boundary Value Problems20150905T00:00:00Z Blowup and nonexistence of solutions of some semilinear degenerate parabolic equations In this paper we study a class of semilinear degenerate parabolic equations arising in mathematical finance and in the theory of diffusion processes. We show that blowup of spatial derivatives of smooth solutions in finite time occurs to initial boundary value problems for a class of degenerate parabolic equations. Furthermore, nonexistence of nontrivial global weak solutions to initial value problems is studied by choosing a special test function. Finally, the phenomenon of blowup is verified by a numerical experiment.MSC: 35K57, 35K65, 35K70.
http://www.boundaryvalueproblems.com/content/2015/1/157
Hui WuBoundary Value Problems 2015, null:15720150905T00:00:00Zdoi:10.1186/s1366101504234/content/figures/s1366101504234toc.gifBoundary Value Problems16872770${item.volume}15720150905T00:00:00ZXML Explicit solutions for a nonclassical heat conduction problem for a semiinfinite strip with a nonuniform heat source A nonclassical initial and boundary value problem for a nonhomogeneous onedimensional heat equation for a semiinfinite material with a zero temperature boundary condition is studied. It is not a standard heat conduction problem because a nonuniform heat source dependent on the heat flux at the boundary is considered. The purpose of this article is to find explicit solutions and analyze how to control their asymptotic temporal behavior through the source term.Explicit solutions independent of the space or temporal variables, solutions with separated variables and solutions by an integral representation depending on the heat flux at the boundary are given. The controlling effects of the source term are analyzed by comparing the asymptotic temporal behavior of solutions corresponding to the same problem with and without source term. Finally, a relationship between the problem considered here with another nonclassical problem for the heat equation is established, and explicit solutions for this second problem are also obtained.In this article, we give explicit solutions and analyze how to control them through the source term for several nonclassical heat equation problems. In addition, our results enable us to compute the asymptotic temporal behavior of the heat flux at the boundary for each explicit solution obtained. As a consequence of our study, several solved nonclassical problems for the heat equation that can be used for testing new numerical methods are given.MSC: 35C05, 35C15, 35C20, 35K55, 45D05, 80A20.
http://www.boundaryvalueproblems.com/content/2015/1/156
Andrea CeretaniDomingo TarziaLuis VillaBoundary Value Problems 2015, null:15620150904T00:00:00Zdoi:10.1186/s1366101504163/content/figures/s1366101504163toc.gifBoundary Value Problems16872770${item.volume}15620150904T00:00:00ZXML On analyticity rate estimates to the magnetohydrodynamic equations in BesovMorrey spaces In this article, we establish higherorder regularizing rate estimates of solutions to generalized magnetohydrodynamic equations in Morrey spaces with initial data
(
u
0
,
d
0
)
in BesovMorrey spaces
N
˙
r
,
λ
,
∞
−
s
×
N
˙
r
,
λ
,
∞
−
s
, where
n
≥
2
,
1
≤
r
<
∞
,
0
≤
λ
<
n
,
r
>
n
−
λ
,
1
2
+
n
−
λ
4
r
<
σ
<
1
+
n
−
λ
4
r
, and
s
=
2
σ
−
1
−
n
−
λ
r
, for which under some smallness condition, the solution of the Cauchy problem is analytic in the spatial variable. Our class of initial data contains strongly singular functions and measures and extends the ones in early work.MSC: 76B03, 76D03.
http://www.boundaryvalueproblems.com/content/2015/1/155
Minghua YangBoundary Value Problems 2015, null:15520150904T00:00:00Zdoi:10.1186/s1366101504172/content/figures/s1366101504172toc.gifBoundary Value Problems16872770${item.volume}15520150904T00:00:00ZXML Periodic solutions of Rayleigh equations with singularities In this paper, we study the existence of periodic solutions of Rayleigh equations with singularities
x
″
+
f
(
t
,
x
′
)
+
g
(
x
)
=
p
(
t
)
. By using the limit properties of the time map, we prove that the given equation has at least one 2π periodic solution.MSC: 34C11, 34C15, 34C25.
http://www.boundaryvalueproblems.com/content/2015/1/154
Zaihong WangTiantian MaBoundary Value Problems 2015, null:15420150904T00:00:00Zdoi:10.1186/s1366101504270/content/figures/s1366101504270toc.gifBoundary Value Problems16872770${item.volume}15420150904T00:00:00ZXML Existence of solutions to nonlinear fractional differential equations with boundary conditions on an infinite interval in Banach spaces In this paper, we consider a system of nonlinear differential equations in a Banach space with boundary conditions on an infinite interval and provide sufficient conditions for the existence of solutions of the system. Our method relies upon the properties of the Kuratowski noncompactness measure and the Sadovskii fixed point theorem. An example is given to illustrate the main results.
http://www.boundaryvalueproblems.com/content/2015/1/153
Jingjing TanCaozong ChengBoundary Value Problems 2015, null:15320150903T12:00:00Zdoi:10.1186/s1366101504190/content/figures/s1366101504190toc.gifBoundary Value Problems16872770${item.volume}15320150903T12:00:00ZXML Universal attractor for nonlinear onedimensional compressible and radiative MHD flow This paper is concerned with the existence of universal attractors in
H
+
i
(
i
=
1
,
2
) for onedimensional compressible and radiative magnetohydrodynamics equations in a bounded domain
Ω
:
=
(
0
,
1
)
. In this paper, the author extends the results in (Qin et al. in J. Differ. Equ. 253:14391488, 2012).MSC: 35B45, 35L65, 35Q60, 76N10.
http://www.boundaryvalueproblems.com/content/2015/1/152
Xin LiuBoundary Value Problems 2015, null:15220150902T12:00:00Zdoi:10.1186/s1366101504136/content/figures/s1366101504136toc.gifBoundary Value Problems16872770${item.volume}15220150902T12:00:00ZXML Modified characteristics projection finite element method for timedependent conductionconvection problems In this paper, we give a modified characteristics projection finite element method for the timedependent conductionconvection problems, which is gotten by combining the modified characteristics finite element method and the projection method. The stability and the error analysis shows that our method is stable and has optimal convergence order. In order to show the effect of our method, some numerical results are presented. From the numerical results, we can see that the modified characteristics projection finite element method can simulate the fluid field, temperature field, and pressure field very well.MSC: 76M10, 65N12, 65N30, 35K61.
http://www.boundaryvalueproblems.com/content/2015/1/151
Zhiyong SiYunxia WangBoundary Value Problems 2015, null:15120150901T00:00:00Zdoi:10.1186/s1366101504207/content/figures/s1366101504207toc.gifBoundary Value Problems16872770${item.volume}15120150901T00:00:00ZXML Existence results for an impulsive SturmLiouville boundary value problems with mixed double parameters In this paper, a class of fourthorder impulsive differential equations depending on two control parameters is investigated. The existence and multiplicity of solutions are obtained by means of the variational methods and the critical point theory. Finally, an example which supports our theoretical results is also presented.
http://www.boundaryvalueproblems.com/content/2015/1/150
Yulin ZhaoLi HuangQiming ZhangBoundary Value Problems 2015, null:15020150829T12:00:00Zdoi:10.1186/s1366101504181/content/figures/s1366101504181toc.gifBoundary Value Problems16872770${item.volume}15020150829T12:00:00ZXML Solutions for perturbed fractional Hamiltonian systems without coercive conditions In this paper we are concerned with the existence of solutions for the following perturbed fractional Hamiltonian systems:
−
t
D
∞
α
(
−
∞
D
t
α
u
(
t
)
)
−
L
(
t
)
u
(
t
)
+
∇
W
(
t
,
u
(
t
)
)
=
f
(
t
)
,
u
∈
H
α
(
R
,
R
n
)
(PFHS), where
α
∈
(
1
/
2
,
1
)
,
t
∈
R
,
u
∈
R
n
,
L
∈
C
(
R
,
R
n
2
)
is a symmetric and positive definite matrix for all
t
∈
R
,
W
∈
C
1
(
R
×
R
n
,
R
)
, and
∇
W
(
t
,
u
)
is the gradient of
W
(
t
,
u
)
at u,
f
∈
C
(
R
,
R
n
)
and belongs to
L
2
(
R
,
R
n
)
. The novelty of this paper is that, assuming
L
(
t
)
is bounded in the sense that there are constants
0
<
τ
1
<
τ
2
<
∞
such that
τ
1

u

2
≤
(
L
(
t
)
u
,
u
)
≤
τ
2

u

2
for all
(
t
,
u
)
∈
R
×
R
n
and
W
(
t
,
u
)
satisfies the AmbrosettiRabinowitz condition and some other reasonable hypotheses,
f
(
t
)
is sufficiently small in
L
2
(
R
,
R
n
)
, we show that (PFHS) possesses at least two nontrivial solutions. Recent results are generalized and significantly improved.MSC: 34C37, 35A15, 35B38.
http://www.boundaryvalueproblems.com/content/2015/1/149
Xionghua WuZiheng ZhangBoundary Value Problems 2015, null:14920150828T00:00:00Zdoi:10.1186/s1366101504065/content/figures/s1366101504065toc.gifBoundary Value Problems16872770${item.volume}14920150828T00:00:00ZXML Boundary value problems for impulsive multiorder Hadamard fractional differential equations In this paper, we study the existence and uniqueness of solutions for impulsive multiorders CaputoHadamard fractional differential equations equipped with boundary and integral conditions. The Banach, Schaefer, and Rothe fixed point theorems and degree theory are used to establish our main results. Examples illustrating the main results are presented.MSC: 34A08, 34B10, 34A37.
http://www.boundaryvalueproblems.com/content/2015/1/148
Weera YukunthornSuthep SuantaiSotiris NtouyasJessada TariboonBoundary Value Problems 2015, null:14820150828T00:00:00Zdoi:10.1186/s1366101504145/content/figures/s1366101504145toc.gifBoundary Value Problems16872770${item.volume}14820150828T00:00:00ZXML