THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM

In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g（μ）＋λf（x）,（x,t）∈Ω×（0,T）,μ=0,（x,t）∈ Ω×[0,T）,μ（x,0）=μ0（x）≥0,x∈Ω.By combining a priori estimate of global solution with property of stationary solution set of problem （P）, we prove that the minimal stationary solution Uλ（x） of problem （P） is stable, whereas, any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem （P）.

Identification of Linear Systems Using Binary Sensors with Random Thresholds

In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered.With the help of stochastic approximation algorithms with expanding truncations,the authors give the recursive estimates for the parameters of both the linear system and the binary sensor.Under reasonable conditions,all constructed estimates are proved to be convergent to the true values with probability one,and the convergence rates are also established.A simulation example is provided to justify the theoretical results.

Bayesian Reliability Assessment and Degradation Modeling with Calibrations and Random Failure Threshold

A degradation model with a random failure threshold is presented for the assessment of reliability by the Bayesian approach. This model is different from others in that the degradation process is proceeding under pre-specified periodical calibrations. And here a random threshold distribution instead of a constant threshold which is difficult to determine in practice is used. The system reliability is defined as the probability that the degradation signals do not exceed the random threshold. Based on the posterior distribution estimates of degradation performance, two models for Bayesian reliability assessments are presented in terms of the degradation performance and the distribution of random failure threshold. The methods proposed in this paper are very useful and practical for multi-stage system with uncertain failure threshold. This study perfects the degradation modeling approaches and plays an important role in the remaining useful life estimation and maintenance decision making.

Stochastic dynamics of the delayed chemostat with Levy noises

This paper formulates and studies a delayed ehemostat with Levy noises.Existence of the glohally positive solution is proved first by establishing suitable Lyapunov functions,and a further result on exact Lyapunov exponent shows the growth of the total concentration in the ehemostat.Then,we prove existence of the uniquely ergodic stationary distribution for a subsystem of the nutrient,based on this,a unique threshold is identified,which completely determines persistence or not of the microorganism in the ehemostat.Besides,recurrence is studied under special conditions in case that the microorganism persists.Results indicate that all the noises have negative effects on persistence of the microorganism,and the time delay has almost no effects on the sample Lyapunov exponent and the threshold value of the ehemostat.