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11.
Julián Fernández Bonder Julio D. Rossi Noemi Wolanski 《Bulletin des Sciences Mathématiques》2006,130(7):565
We study the dependence on the subset A⊂Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measure. In the case that Ω is a ball we prove that there exists an optimal hole that is spherically symmetric. In the case p=2 we prove that every optimal hole is spherically symmetric. Then, we study the behavior of the best constant when the hole is allowed to have zero Lebesgue measure. We show that this constant depends continuously on the subset and we discuss when it is equal to the Sobolev trace constant without the vanishing restriction. 相似文献
12.
ABSTRACTIn this paper we study a nonlocal diffusion problem on a manifold. These kinds of equations can model diffusions when there are long range effects and have been widely studied in Euclidean space. We first prove existence and uniqueness of solutions and a comparison principle. Then, for a convenient rescaling we prove that the operator under consideration converges to a multiple of the usual Heat-Beltrami operator on the manifold. Next, we look at the long time behavior on compact manifolds by studying the spectral properties of the operator. Finally, for the model case of hyperbolic space we study the long time asymptotics and find a different and interesting behavior. 相似文献
13.
Qiaofeng Xie Bing Wang Haocheng Wen Wei He Piotr Wolanski 《Proceedings of the Combustion Institute》2019,37(3):3425-3432
The enhancement of continuously rotating detonation in oxygen-enriched air was demonstrated in an annular rotating detonation combustor (RDC) under a diffusive supply of hydrogen and an oxidizer. Experimental tests were performed to reveal the effects of oxygen volume fraction, mass flow rate, and equivalent ratio on the propagation of continuously rotating detonation wave (CRDW). It is observed that an increase in the air mass flow rate from 25 g/s to 225 g/s causes an increase in the propagation velocity of the stable CRDW in the RDC. For an oxygen volume fraction up to 35%, the difference between the propagation velocity of detonation and the theoretical Chapman–Jouguet value is less than 5%. Under the chemical stoichiometric ratio condition for air, the CRDW is stabilized when the air mass flow rate reaches 185 g/s. However, stabilized CRDW is observed even when the air flow rate is only 45 g/s under the presence of 30% or 35% oxygen. Increase in the oxygen volume fraction leads to an extension of the rich/lean limit for generating a stable CRDW. This study aims to provide guidance for the modulation of continuously rotating detonation. 相似文献
14.
C. Lederman J. L. Vá zquez N. Wolanski 《Transactions of the American Mathematical Society》2001,353(2):655-692
We investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function defined in a domain and such that
0\}. \end{displaymath}">
We also assume that the interior boundary of the positivity set, \nobreak 0\}$">, so-called free boundary, is a regular hypersurface on which the following conditions are satisfied:
Here denotes outward unit spatial normal to the free boundary. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of . This problem arises in combustion theory as a limit situation in the propagation of premixed flames (high activation energy limit).
The problem admits classical solutions only for good data and for small times. Several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. We investigate conditions under which the three concepts agree and produce a unique solution.
15.
Fundamentals of rotating detonations 总被引:17,自引:0,他引:17
A rotating detonation propagating at nearly Chapman–Jouguet velocity is numerically stabilized on a two-dimensional simple
chemistry flow model. Under purely axial injection of a combustible mixture from the head end of a toroidal section of coaxial
cylinders, the rotating detonation is proven to give no average angular momentum at any cross section, giving an axial flow.
The detonation wavelet connected with an oblique shock wave ensuing to the downstream has a feature of unconfined detonation,
causing a deficit in its propagation velocity. Due to Kelvin–Helmholtz instability existing on the interface of an injected
combustible, unburnt gas pockets are formed to enter the junction between the detonation and oblique shock waves, generating
strong explosions propagating to both directions. Calculated specific impulse is as high as 4,700 s.
相似文献
16.
Abstract. Ignition of a liquid layer and dust fuel layer by a detonation wave propagating in hydrogen-oxygen and acetylene-oxygen mixtures
is reported. Experiments were carried out using a shock tube equipped with optical-quality observation windows. A schlieren
system and a high-speed camera were used for measurements of ignition delay. Pressure transducers provided data necessary
for measurements of the detonation wave velocity and pressure variation within the front of the interacted detonation wave
and fuel layer. Kerosene, nitroglycerin and PETN were used as fuels. Investigation shows that the layer of liquid fuel can
be efficiently ignited by detonation wave. It was found that the ignition delay of the fuel layer depends mostly on the detonation
wave velocity and sensitivity of igniting fuels, and slightly on the layer thickness.
Received 12 August 2001 / Accepted 1 July 2002 Published online 4 February 2003
Correspondence to: P. Wolanski (e-mail: wolanski@itc.pw.edu.pl)
An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems
at Seattle, USA, from July 29 to August 3, 2001 相似文献
17.
In this paper we prove a local monotonicity formula for solutions to an inhomogeneous singularly perturbed diffusion problem
of interest in combustion. This type of monotonicity formula has proved to be very useful for the study of the regularity
of limits u of solutions of the singular perturbation problem and of ∂{u > 0}, in the global homogeneous case. As a consequence of this formula we prove that u has an asymptotic development at every point in ∂{u > 0} where there is a nonhorizontal tangent ball. These kind of developments have been essential for the proof of the regularity
of ∂{u > 0} for Bernoulli and Stefan free boundary problems. We also present applications of our results to the study of the regularity
of ∂{u > 0} in the stationary case including, in particular, its regularity in the case of energy minimizers. We present as well
a regularity result for traveling waves of a combustion model that relies on our monotonicity formula and its consequences.The
fact that our results hold for the inhomogeneous problem allows a very wide applicability. Indeed, they may be applied to
problems with nonlocal diffusion and/or transport.
The research of the authors was partially supported by Fundación Antorchas Project 13900-5, Universidad de Buenos Aires grant
X052, ANPCyT PICT No 03-13719, CONICET PIP 5478. The authors are members of CONICET. 相似文献
18.
We study the following two phase elliptic singular perturbation problem:
Δuε=βε(uε)+fε,