1,002 research outputs found
Self-similar solutions of the p-Laplace heat equation: the case when p>2
We study the self-similar solutions of the equation in when We make a complete study
of the existence and possible uniqueness of solutions of the form of any sign, regular
or singular at Among them we find solutions with an expanding compact
support or a shrinking hole (for or a spreading compact support or a
focussing hole (for When we show the existence of positive
solutions oscillating around the particular solution $U(x,t)=C_{N,p}(| x|
^{p}/(-t))^{1/(p-2)}.
A new dynamical approach of Emden-Fowler equations and systems
We give a new approach on general systems of the form (G){[c]{c}%
-\Delta_{p}u=\operatorname{div}(|\nabla u| ^{p-2}\nabla u)=\epsilon_{1}|x|
^{a}u^{s}v^{\delta}, -\Delta_{q}v=\operatorname{div}(|\nabla v|^{q-2}\nabla
u)=\epsilon_{2}|x|^{b}u^{\mu}v^{m}, where are
real parameters, and In
the radial case we reduce the problem to a quadratic system of order 4, of
Kolmogorov type. Then we obtain new local and global existence or nonexistence
results. In the case we also describe the
behaviour of the ground states in two cases where the system is variational. We
give an important result on existence of ground states for a nonvariational
system with and In the nonradial case we solve a conjecture of
nonexistence of ground states for the system with and and
Comment: 43 page
Evolution equations of p-Laplace type with absorption or source terms and measure data
Let be a bounded domain of , and We consider problems\textit{ }of the type % \left\{
\begin{array} [c]{l}% {u_{t}}-{\Delta_{p}}u\pm\mathcal{G}(u)=\mu\qquad\text{in
}Q,\\ {u}=0\qquad\text{on }\partial\Omega\times(0,T),\\
u(0)=u_{0}\qquad\text{in }\Omega, \end{array} \right. where
is the -Laplacian, is a bounded Radon measure, and is an absorption or a source term In
the model case
or has an exponential type. We prove the existence of
renormalized solutions for any measure in the subcritical case, and give
sufficient conditions for existence in the general case, when is good in
time and satisfies suitable capacitary conditions.Comment: arXiv admin note: substantial text overlap with arXiv:1310.525
Pointwise estimates and existence of solutions of porous medium and -Laplace evolution equations with absorption and measure data
Let be a bounded domain of . We obtain a
necessary and a sufficient condition, expressed in terms of capacities, for
existence of a solution to the porous medium equation with absorption
\begin{equation*} \left\{ \begin{array}{l} {u_{t}}-{\Delta
}(|u|^{m-1}u)+|u|^{q-1}u=\mu ~ \text{in }\Omega \times (0,T), \\
{u}=0~~~\text{on }\partial \Omega \times (0,T), \\ u(0)=\sigma , \end{array}
\right. \end{equation*} where and are bounded Radon measures,
, . We also obtain a sufficient condition for
existence of a solution to the -Laplace evolution equation \begin{equation*}
\left\{ \begin{array}{l} {u_{t}}-{\Delta _{p}}u+|u|^{q-1}u=\mu ~~\text{in
}\Omega \times (0,T), \\ {u}=0 ~ \text{on }\partial \Omega \times (0,T), \\
u(0)=\sigma . \end{array} \right. \end{equation*} where and
Stability properties for quasilinear parabolic equations with measure data
Let be a bounded domain of , and We study problems of the model type \left\{ \begin{array}
[c]{l}% {u_{t}}-{\Delta_{p}}u=\mu\qquad\text{in }Q,\\ {u}=0\qquad\text{on
}\partial\Omega\times(0,T),\\ u(0)=u_{0}\qquad\text{in }\Omega, \end{array}
\right. where , and Our main result is a \textit{stability theorem }extending the
results of Dal Maso, Murat, Orsina, Prignet, for the elliptic case, valid for
quasilinear operators div\textit{. }Comment: arXiv admin note: substantial text overlap with arXiv:1310.525
On the connection between two quasilinear elliptic problems with source terms of order 0 or 1
We establish a precise connection between two elliptic quasilinear problems
with Dirichlet data in a bounded domain of The first one, of
the form
involves a source gradient term with natural growth, where is
nonnegative, , and is a nonnegative measure. The
second one, of the form
presents a source term of order where is nondecreasing, and is a
nonnegative measure. Here and can present an asymptote. The
correlation gives new results of existence, nonexistence, regularity and
multiplicity of the solutions for the two problems, without or with measures.
New informations on the extremal solutions are given when is superlinear
Initial trace of solutions of Hamilton-Jacobi parabolic equation with absorption
Here we study the initial trace problem for the nonnegative solutions of the
equation in
where
and or is a smooth bounded domain of
and on We can
define the trace at as a nonnegative Borel measure where is the closed set where it is infinite, and is a
Radon measure on We show that the trace is a
Radon measure when For and any given Borel
measure, we show the existence of a minimal solution, and a maximal one on
conditions on When and
is an open subset of the existence extends to any
when and any when . In
particular there exists a self-similar nonradial solution with trace
with a growth rate of order as for fixed
Moreover we show that the solutions with trace in
may present near a growth rate of order
in and of order on $\partial
\omega.
Separable solutions of some quasilinear equations with source reaction
We study the existence of singular separable solutions to a class of
quasilinear equations with reaction term. In the 2-dim case, we use a dynamical
system approach to construct our solutions.Comment: 34 page
THE INFLUENCE OF THERMAL LOADING ON THE LEAK TIGHTNESS BEHAVIOUR OF HORIZONTALLY SPLIT CENTRIFUGAL COMPRESSORS
LectureFor the purpose of maintenance requirements or for some applications in the chemical industry (for instance chlorine) the centrifugal compressor must be designed with a horizontally (axially) split casing.
Beyond the decision about the type of manufacturing (cast or welded) or about the material selection one of the utmost issues regarding the design of the compressor lies in the leak tightness of the flanges. The design of the compressor casing needs detailed checking for tightness. In order to ensure a proper design with respect to integrity of stress and tightness under test and operating conditions several FE Analyses and resulting criteria have been developed by the OEMs. Furthermore in order to demonstrate the leak tightness the casing is subjected to a hydrostatic test prior to the assembly of the inner parts and rotor. According the API specification a hydrostatic pressure of at least 1.5 times maximum design pressure is applied. This standard procedure is usually considered to be sufficient for demonstrating the casing integrity, the tightness in operation and to check the accuracy of the FE analysis.
However some applications require the use of several sections (consisting of some stages) inside one casing. According to the stage configuration hot and cold casing sections might be close to each other. In operation the compressor casing is subjected not only to pressure but also to thermal loading. These potential high temperature gradients can considerably influence the compressor behaviour regarding its tightness. The conventional hydrostatic test can even be less critical than at some particular operating conditions of the compressor on site.
This paper describes some experiences of the author’s company with this type of compressors and the performed calculations. Different configurations are analysed and compared between each others. The paper shows the steps for the optimization of casings in order to develop an appropriate split line flange design supported by FE calculations. Some examples of different casing concepts are shown and discussed. At last the paper highlights some decisive issues which influence the tightness of compressor like:
- Design of inner casing - Arrangement of sections - Geometry of flange - Design and arrangement of bolts
- …