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### Open Access Journals

CPAA

In this paper, we first derive an equation
for a single species population with two age stages and a fixed
maturation period living in the half plane such as ocean and
big lakes.
By adopting the compact open topology, we establish some a priori
estimate for nontrivial solutions after describing asymptotic properties
of the nonlocal delayed effect, which enables us to show the
permanence of the equation. Then we can employ standard
dynamical system theoretical arguments to establish the global
dynamics of the equation under appropriate conditions. Applying
the main results to the model with Ricker's birth function and
Mackey-Glass's hematopoiesis function, we obtain threshold results
for the global dynamics of these two models.

CPAA

We study the initial and initial-boundary value problems
for the $p$-th power Newtonian fluid in one space dimension
with general large initial data.
The existence and uniqueness of globally smooth non-vacuum solutions
are established when the thermal conductivity
is some non-negative power of the temperature.
Our analysis is based on some detailed estimates on
the bounds of both density and temperature.

KRM

This paper is concerned with nonlinear stability of viscous shock profiles for the one-dimensional
isentropic compressible Navier-Stokes equations. For the case when the diffusion wave introduced in
[6, 7] is excluded, such a problem has been studied in [5, 11] and local
stability of weak viscous shock profiles is well-established, but for the corresponding result with large
initial perturbation, fewer results have been obtained. Our main purpose is to deduce the corresponding
nonlinear stability result with large initial perturbation by exploiting the elementary energy method. As a
first step toward this goal, we show in this paper that for certain class of ``large" initial perturbation
which can allow the initial density to have large oscillation, similar stability result still holds. Our
analysis is based on the continuation argument and the technique developed by Kanel' in
[4].

KRM

The Cauchy problem to the Fokker-Planck-Boltzmann equation under Grad's angular cut-off assumption is investigated.
When the initial data is a small perturbation of an equilibrium state, global existence and optimal temporal decay estimates
of classical solutions are established. Our analysis is based on the coercivity of the Fokker-Planck operator
and an elementary weighted energy method.

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