Propagation of Singularities of Nonlinear Heat Flow in Fissured Media

In this paper we investigate the propagation of singularities in a nonlinear parabolic equation with strong absorption when the absorption potential is strongly degenerate following some curve in the $(x,t)$ space. As a very simplified model, we assume that the heat conduction is constant but the absorption of the media depends stronly of the characteristic of the media. More precisely we suppose that the temperature $u$ is governed by the following equation \label{I-1} \partial_{t}u-\Delta u+h(x,t)u^p=0\quad \text{in}Q_{T}:=R^N\times (0,T) where $p>1$ and $h\in C(\bar Q_{T})$. We suppose that $h(x,t)>0$ except when $(x,t)$ belongs to some space-time curve.Comment: To appear in Comm. Pure Appl. Ana

Admissible initial growth for diffusion equations with weakly superlinear absorption

We study the admissible growth at infinity of initial data of positive solutions of \prt\_t u-\Gd u+f(u)=0 in \BBR\_+\ti\BBR^N when $f(u)$ is a continuous function, {\it mildly} superlinear at infinity, the model case being f(u)=u\ln^\ga (1+u) with 1\textless{}\ga\textless{}2. We prove in particular that if the growth of the initial data at infinity is too strong, there is no more diffusion and the corresponding solution satisfies the ODE problem \prt\_t \gf+f(\gf)=0 on \BBR\_+ with \gf(0)=\infty.Comment: Communications in Contemporary Mathematics, to appea

Singular solutions of some nonlinear parabolic equations with spatially inhomogeneous absorption

We study the limit behaviour of solutions of a class of solutions of nonlinear parabolic equations with a degenerate strong absorption. We prove that two types of phenomena can occur: the pointwise singularity or the formation of razor blades (or persistent singularities).Comment: 29 page

Performance of Network and Service Monitoring Frameworks

The efficiency and the performance of anagement systems is becoming a hot research topic within the networks and services management community. This concern is due to the new challenges of large scale managed systems, where the management plane is integrated within the functional plane and where management activities have to carry accurate and up-to-date information. We defined a set of primary and secondary metrics to measure the performance of a management approach. Secondary metrics are derived from the primary ones and quantifies mainly the efficiency, the scalability and the impact of management activities. To validate our proposals, we have designed and developed a benchmarking platform dedicated to the measurement of the performance of a JMX manager-agent based management system. The second part of our work deals with the collection of measurement data sets from our JMX benchmarking platform. We mainly studied the effect of both load and the number of agents on the scalability, the impact of management activities on the user perceived performance of a managed server and the delays of JMX operations when carrying variables values. Our findings show that most of these delays follow a Weibull statistical distribution. We used this statistical model to study the behavior of a monitoring algorithm proposed in the literature, under heavy tail delays distribution. In this case, the view of the managed system on the manager side becomes noisy and out of date

Diffusion versus absorption in semilinear elliptic equations

International audienceWe study the limit behaviour of a sequence of singular solutions of a nonlinear elliptic equation with a strongly degenerate absorption term at the boundary of the domain. We give sharp conditions on the level of degeneracy in order the pointwise singularity not to propagate along the boundary

Diffusion versus absorption in semilinear parabolic equations

We study the limit, when $k\to\infty$, of the solutions $u=u_{k}$ of (E) \prt_{t}u-\Delta u+ h(t)u^q=0 in \BBR^N\ti (0,\infty), $u_{k}(.,0)=k\delta_{0}$, with $q>1$, $h(t)>0$. If h(t)=e^{-\gw(t)/t} where \gw>0 satisfies to \int_{0}^1\sqrt{\gw(t)}t^{-1}dt1 and \prt_{t}u-\Gd u+ h(t)e^{u}=0

The balance between diffusion and absorption in semilinear parabolic equations

Let $h:[0,\infty)\mapsto [0,\infty)$ be continuous and nondecreasing, $h(t)>0$ if $t>0$, and $m,q$ be positive real numbers. We investigate the behavior when $k\to\infty$ of the fundamental solutions $u=u_{k}$ of \prt_{t} u-\Delta u^m+h(t)u^q=0 in \Omega\ti (0,T) satisfying $u_{k}(x,0)=k\delta_0$. The main question is wether the limit is still a solution of the above equation with an isolated singularity at $(0,0)$, or a solution of the associated ordinary differential equation $u'+h(t)u^q=0$ which blows-up at $t=0$

Forecast combination for U.S. recessions with real-time data

This paper proposes the use of forecast combination to improve predictive accuracy in forecasting the U.S. business cycle index, as published by the Business Cycle Dating Committee of the NBER. It focuses on one-step ahead out-of-sample monthly forecast utilising the well-established coincident indicators and yield curve models, allowing for dynamics and real-time data revisions. Forecast combinations use logscore and quadratic-score based weights, which change over time. This paper finds that forecast accuracy improves when combining the probability forecasts of both the coincident indicators model and the yield curve model, compared to each model's own forecasting performance

Practical considerations for optimal weights in density forecast combination

The problem of finding appropriate weights to combine several density forecasts is an important issue currently debated in the forecast combination literature. Recently, a paper by Hall and Mitchell (IJF, 2007) proposes to combine density forecasts with optimal weights obtained from solving an optimization problem. This paper studies the properties of this optimization problem when the number of forecasting periods is relatively small and finds that it often produces corner solutions by allocating all the weight to one density forecast only. This paper’s practical recommendation is to have an additional training sample period for the optimal weights. While reserving a portion of the data for parameter estimation and making pseudo-out-of-sample forecasts are common practices in the empirical literature, employing a separate training sample for the optimal weights is novel, and it is suggested because it decreases the chances of corner solutions. Alternative log-score or quadratic-score weighting schemes do not have this training sample requirement. Januar