Polynomial Decay and Blow Up of Solutions for Variable Coefficients Viscoelastic Wave Equation with Acoustic Boundary Conditions

A variable coefficient viscoelastic wave equation with acoustic boundary conditions and nonlinear source term is considered. Under suitable conditions on the initial data and the relaxation function g, we show the polynomial decay of the energy solution and the blow up of solutions by energy methods. The estimates for the lifespan of solutions are also given.

Assessment of dairy cow feed intake based on BP neural network with polynomial decay learning rate

To overcome the shortcomings of traditional dairy cow feed intake assessment model andBP neural network, this paper proposes a method of optimizing BP neural network usingpolynomial decay learning rate, taking the cow’s body weight, lying duration, lying times,walking steps, foraging duration and concentrate-roughage ratio as input variables andtaking the actual feed intake is the output variable to establish a dairy cow feed intakeassessment model, and the model is trained and verified by experimental data collectedon site. For the sake of comparative study, feed intake is simultaneously assessed by SVRmodel, KNN logistic regression model, traditional BP neural network model, and multilayerBP neural network model. The results show that the established BP model using the polynomial decay learning rate has the highest assessment accuracy, the MSPE, RMSE, MAE,MAPE and R2 are 0.043 kg2/d and 0.208 kg/d, 0.173 kg/d, 1.37% and 0.94 respectively. Compared with SVR model and KNN mode, the RMSE value reduced by 43.9% and 26.5%, it isalso found that the model designed in this paper has many advantages in comparison withthe BP model and multilayer BP model in terms of precision and generalization. Therefore,this method is ready to be applied for accurately evaluating the dairy cow feed intake, andit can provide theoretical guidance and technical support for the precise-feeding and canalso be of high significance in the improvement of dairy precise-breeding.

GLOBAL EXISTENCE, UNIFORM DECAY AND EXPONENTIAL GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING

In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.

Asymptotic Behavior of a Bi-Dimensional Hybrid System

We study the asymptotic behavior of the solutions of a Hybrid System wrapping an elliptic operator.

Convergence and error estimate of cascade algorithms with infinitely supported masks in L_p(R^s)

The cascade algorithm plays an important role in computer graphics and wavelet analysis.In this paper,we first investigate the convergence of cascade algorithms associated with a polynomially decaying mask and a general dilation matrix in L p (R s) (1 p ∞) spaces,and then we give an error estimate of the cascade algorithms associated with truncated masks.It is proved that under some appropriate conditions if the cascade algorithm associated with a polynomially decaying mask converges in the L p-norm,then the cascade algorithms associated with the truncated masks also converge in the L p-norm.Moreover,the error between the two resulting limit functions is estimated in terms of the masks.