The initial boundary value problem for the fourth-order wave equation u_(tt)+△~2u+u=|u|^(p-1)u is considered.The existence and uniqueness of global weak solutions is obtained by using the Galerkin method and the conc...The initial boundary value problem for the fourth-order wave equation u_(tt)+△~2u+u=|u|^(p-1)u is considered.The existence and uniqueness of global weak solutions is obtained by using the Galerkin method and the concept of stable set due to Sattinger.展开更多
Non-liner wave equation inversion,wavelet analysis and artificial neural networks were used to obtain stratum parameters and the distribution of thin coal seams.The lithology of the water-bearing/resisting layer in th...Non-liner wave equation inversion,wavelet analysis and artificial neural networks were used to obtain stratum parameters and the distribution of thin coal seams.The lithology of the water-bearing/resisting layer in the Quaternary system was also predicted.The implementation process included calculating the well log parameters,stratum contrasting the seismic data and the well logs,and extracting,studying and predicting seismic attributes.Seismic inversion parameters,including the layer velocity and wave impedance,were calculated and effectively used for prediction and analysis.Prior knowledge and seismic interpretation were used to remedy a dearth of seismic data during the inversion procedure.This enhanced the stability of the inversion method.Non-linear seismic inversion and artificial neural networks were used to interpret coal seismic lithology and to study the water-bearing/resisting layer in the Quaternary system.Interpretation of the 1～2 m thin coal seams,and also of the water-bearing/resisting layer in the Quaternary system,is provided.The upper mining limit can be lifted from 60 m to 45 m.The predictions show that this method can provide reliable data useful for thin coal seam exploitation and for lifting the upper mining limit,which is one of the principles of green mining.展开更多
This paper considers the following Cauchy problem for semilinear wave equations in n space dimensionswhere A is the wave operator, F is quadratic in (?) with (?) = ( ).The minimal value of s is determined such that th...This paper considers the following Cauchy problem for semilinear wave equations in n space dimensionswhere A is the wave operator, F is quadratic in (?) with (?) = ( ).The minimal value of s is determined such that the above Cauchy problem is locally well-posed in H8. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n≥5). The purpose of this paper is to supplement with a proof in the case n = 2,4.展开更多
基金the National Natural Science Foundation of China(10301026)the Research Foundation of Chengdu University of Information Technology(CRF200702)
文摘The initial boundary value problem for the fourth-order wave equation u_(tt)+△~2u+u=|u|^(p-1)u is considered.The existence and uniqueness of global weak solutions is obtained by using the Galerkin method and the concept of stable set due to Sattinger.
基金Projects 40574057 and 40874054 supported by the National Natural Science Foundation of ChinaProjects 2007CB209400 by the National Basic Research Program of ChinaFoundation of China University of Mining and Technology (OF4471)
文摘Non-liner wave equation inversion,wavelet analysis and artificial neural networks were used to obtain stratum parameters and the distribution of thin coal seams.The lithology of the water-bearing/resisting layer in the Quaternary system was also predicted.The implementation process included calculating the well log parameters,stratum contrasting the seismic data and the well logs,and extracting,studying and predicting seismic attributes.Seismic inversion parameters,including the layer velocity and wave impedance,were calculated and effectively used for prediction and analysis.Prior knowledge and seismic interpretation were used to remedy a dearth of seismic data during the inversion procedure.This enhanced the stability of the inversion method.Non-linear seismic inversion and artificial neural networks were used to interpret coal seismic lithology and to study the water-bearing/resisting layer in the Quaternary system.Interpretation of the 1～2 m thin coal seams,and also of the water-bearing/resisting layer in the Quaternary system,is provided.The upper mining limit can be lifted from 60 m to 45 m.The predictions show that this method can provide reliable data useful for thin coal seam exploitation and for lifting the upper mining limit,which is one of the principles of green mining.
基金Project supported by the 973 Project of the National Natural Science Foundation of China,the Key Teachers Program and the Doctoral Program Foundation ofthe Miistry of Education of China.
文摘This paper considers the following Cauchy problem for semilinear wave equations in n space dimensionswhere A is the wave operator, F is quadratic in (?) with (?) = ( ).The minimal value of s is determined such that the above Cauchy problem is locally well-posed in H8. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n≥5). The purpose of this paper is to supplement with a proof in the case n = 2,4.
