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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...
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...
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, and being the identity
operator and the Laplacian) which generates an initial-boundary value problem
with an explicit formula of the solution . In the paper, the result is obtained
not just for the operator , but also for an arbitrary parabolic differential
operat...
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...
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 ...
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 domains
Springer Science and Business Media LLC -
AbstractThe 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 , ∞ ) , under the mixed boundary condition on a bounded domain Ω. In fact,
this has remained an...
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 ( ) instead of being
translation compact. By applying some new results and the energy estimate
technique, the existence of uniform attractors is obtained. The result improves
and extends some k...
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. ...
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