Donghao Li

In this paper, the wave equation with logarithmic damping is considered. The global existence of solutions is proved by means of Faedo-Galerkin combined with the stable set method. By using multiplier method, integral inequalities, and special algebraic inequalities, the exponential decay of energy is obtained. Finally, the blow-up in finite time under some conditions on initial data is given. These contributions complement existing literature on logarithmic damping, which is an area that remains relatively unexplored.

In this paper, a semilinear wave equation with logarithmic feedback is considered. The polynomial decay of the energy is obtained. The method of proof is based on multipliers technique, on a integral inequality, and on some special algebraic inequalities. The results complement those of the literature about logarithmic damping, and it seem to be an interesting problem in the unknown land of weak damping mechanics.

Energy conservation is an important means for enterprises to reduce costs and increase efficiency. The fuel ethanol production process involves multiple process units, including biochemical reaction, ethanol separation, and co product DDGS feed production, which requires a large amount of energy consumption and correspondingly generates a large amount of waste heat. The comprehensive utilization of waste heat through thermal coupling technology can significantly reduce heat energy consumption, save production costs and improve the comprehensive benefits of enterprises. This paper focuses on the application of least square method to explore the preparation of C by ethanol coupling_ 4. The optimum conditions of olefins were studied to explore the process conditions of ethanol catalytic coupling to olefins By comparing the relationship between the variable and olefin yield when only the variable is changed, the experimental data are interpolated by using Matlab and Mathematica mathematical software to fit the relationship curve, and a model of least square method is established to guide production Comparing the obtained functional relationship with the experimental data, the simulation error is within an acceptable range. The established model can better predict the olefin yield under different variables The results showed that the conversion of ethanol could reach 99.03%, C₄ olefin selectivity could reach 58.09%, and the yield could reach 57.52% without limiting the reaction temperature; Under the condition that the reaction temperature must be less than 350°C, the ethanol conversion rate can reach 54.33%, C₄ olefin selectivity can reach 38.52%, and the production yield can reach 20.93%. Finally, it is found that temperature has an important impact on production, and the maximum temperature should be maintained during actual production. It is expected to provide reference for the development of China's fuel ethanol industry.

The initial-boundary value problem for a wave equation with nonlinear averaged damping and nonlocal nonlinear source term is considered. We provide the sufficient conditions of finite time blow-up fo...

The viscoelastic wave equation with nonlinear nonlocal weak damping is considered. The local existence of solutions is established. Under arbitrary positive initial energy, a finite-time blow-up result is proved by a new modified concavity method.

In this paper, we consider a nonlinear viscoelastic equation with nonlocal nonlinear boundary damping and two nonlinear source terms (boundary and interior). We obtain the global existence of solution via the potential well method. By introducing suitable Lyapunov functionals, using the multiplier method, and constructing convex differential inequality, we establish an explicit and general decay rate result. This improves previous decay results concerning the problem. We also get a finite time blow-up result of solution with positive initial energy under suitable conditions on the initial data and positive memory function. This is the first result for blow-up of the problem with nonlocal nonlinear boundary damping.