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Existence of positive solutions for a third-order multipoint boundary value problem and extension to fractional case
Springer Science and Business Media LLC - Tập 2016 - Trang 1-11 - 2016
In this paper, we study a nonlinear third-order multipoint boundary value problem by the monotone iterative method. We then obtain the existence of monotone positive solutions and establish iterative schemes for approximating the solutions. In addition, we extend the considered problem to the Riemann-Liouville-type fractional analogue. Finally, we give a numerical example for demonstrating the eff...... hiện toàn bộ
Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions
Springer Science and Business Media LLC - Tập 2020 - Trang 1-13 - 2020
In this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it foll...... hiện toàn bộ
On explicit and numerical solvability of parabolic initial-boundary value problems
Springer Science and Business Media LLC - Tập 2006 - Trang 1-12 - 2006
A homogeneous boundary condition is constructed for the parabolic equation
in an arbitrary cylindrical domain
(
being a bounded domain,
...... hiện toàn bộ
On an electrorheological fluid equation with orientated convection term
Springer Science and Business Media LLC - Tập 2019 Số 1 - 2019
Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium
Springer Science and Business Media LLC - Tập 2021 - Trang 1-15 - 2021
We consider the inertial Qian–Sheng’s Q-tensor dynamical model for the nematic liquid crystal flow, which can be viewed as a system coupling the hyperbolic-type equations for the Q-tensor parameter with the incompressible Navier–Stokes equations for the fluid velocity. We prove the existence and uniqueness of local in time strong solutions to the system with the initial data near uniaxial equilibr...... hiện toàn bộ
Global existence of weak solution for the compressible Navier–Stokes–Poisson system with density-dependent viscosity
Springer Science and Business Media LLC - Tập 2019 - Trang 1-40 - 2019
In this paper, we are concerned with the existence of global weak solutions to the compressible Navier–Stokes–Poisson equations with the non-flat doping profile when the viscosity coefficients are density-dependent, the data are large and spherically symmetric, and we focus on the case where those coefficients vanish in vacuum. We construct a suitable approximate system and consider it in annular ...... hiện toàn bộ
The Solution of Two-Point Boundary Value Problem of a Class of Duffing-Type Systems with Non- Perturbation Term
Springer Science and Business Media LLC - Tập 2009 - Trang 1-12 - 2009
This paper deals with a two-point boundary value problem of a class of Duffing-type systems with non-
perturbation term. Several existence and uniqueness theorems were presented.
A necessary and sufficient condition for the existence of global solutions to reaction-diffusion equations on bounded domainsAbstract The purpose of this paper is to give a necessary and sufficient condition for the existence and non-existence of global solutions of the following semilinear parabolic equations $$ u_{t}=\Delta u+\psi (t)f(u),\quad \text{in }\Omega \times (0,\infty ), $$
u
t
=
Δ
u
+
ψ
(
t
)
f
(
u
)
,
in
Ω
×
(
0
,
∞
)
,
$f(u)=u^{p}$
f
(
u
)
=
u
p
$$ \begin{aligned} & \text{there is no global solution for any initial data if and only if } \\ & \int _{0}^{\infty}\psi (t) \frac{f (\lVert S(t)u_{0}\rVert _{\infty} )}{\lVert S(t)u_{0}\rVert _{\infty}}\,dt= \infty \\ &\text{for every nonnegative nontrivial initial data } u_{0}\in C_{0}( \Omega ). \end{aligned} $$
there is no global solution for any initial data if and only if
∫
0
∞
ψ
(
t
)
f
(
∥
S
(
t
)
u
0
∥
∞
)
∥
S
(
t
)
u
0
∥
∞
d
t
=
∞
for every nonnegative nontrivial initial data
u
0
∈
C
0
(
Ω
)
.
$(S(t))_{t\geq 0}$ hiện toàn bộ
Springer Science and Business Media LLC -
Uniform attractors for non-autonomous suspension bridge-type equations
Springer Science and Business Media LLC - Tập 2014 - Trang 1-14 - 2014
We discuss the long-time dynamical behavior of the non-autonomous suspension bridge-type equation, where the nonlinearity
is translation compact and the time-dependent external forces
only satisfy Condition (
...... hiện toàn bộ
A new kind of double Chebyshev polynomial approximation on unbounded domains
Springer Science and Business Media LLC - Tập 2013 - Trang 1-13 - 2013
In this study, a new solution scheme for the partial differential equations with variable coefficients defined on a large domain, especially including infinities, has been investigated. For this purpose, a spectral basis, called exponential Chebyshev (EC) polynomials, has been extended to a new kind of double Chebyshev polynomials. Many outstanding properties of those polynomials have been shown. ...... hiện toàn bộ
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