Pullback attractors for the non-autonomous complex Ginzburg–Landau type equation with p-Laplacian

In this paper, we are concerned with the long-time behavior of the non-autonomous complex Ginzburg–Landau type equation with p-Laplacian. We first prove the existence of pullback absorbing sets in L2(Ω)∩W01,p(Ω)∩Lq(Ω) for the process {U(t,τ)}t⩾τ corresponding to the non-autonomous complex Ginzburg–Landau type equation with p-Laplacian. Next, the existence of a pullback attractor in L2(Ω) is established by the Sobolev compactness embedding theorem. Finally, we prove the existence of a pullback attractor in W01,p(Ω) for the process {U(t,τ)}t⩾τ by asymptotic a priori estimates

Insensitizing controls for a fourth order semi-linear parabolic equations

This paper is concerned with the existence of insensitizing controls for a fourth order semilinear parabolic equation. Here, the initial data is partially unknown, we would like to find controls such that a specific functional is insensitive for small perturbations of the initial data. In general, this kind of problems can be recast as a null controllability problem for a nonlinear cascade system. We will first prove a null controllability result for a linear problem by global Carleman estimates and dual arguments. Then, by virtue of Leray-Schauder's fixed points theorem, we conclude the null controllability for the cascade system in the semi-linear case.Comment: arXiv admin note: text overlap with arXiv:2211.00428, arXiv:2211.0064

An investigation of air and water dual adjustment decoupling control of surface heat exchanger

The terminal equipment of central cooling system accounts for a significant proportion of the total system's energy consumption. Therefore, it is important to reduce the terminal equipment energy consumption in central air conditioning system. In this study, the difference of the effect of the chilled water flow rate and air supply rate on the surface cooler during the heat transfer process is taken into full account. Matlab/Simulink simulation software is used to model and simulate the heat transfer of surface cooler of the main terminal equipment of air conditioning system. Simulation tests and experimental validations are conducted by using variable chilled water flow rate and variable air supply rate control mode separately. The experiment results show that the simulation model can effectively predict the heat transfer performance of heat exchanger. Further, the study introduced a dual feedback control mode, which synchronously regulates the chilled water flow rate and air supply rate. Also, under certain conditions, the complex heat transfer process of the surface cooler can be decoupled, and single variable control pattern is used to separately regulate the chilled water flow rate and air supply rate. This can effectively shorten the system regulation time, reduce overshoot and improve control performance