Based on the open stope method,the stability of the gob area was decided bypillars and stiff roof.Therefore,it was dispensable to leave pillars with long-term strengthand enough size to support the stiff roof during m...Based on the open stope method,the stability of the gob area was decided bypillars and stiff roof.Therefore,it was dispensable to leave pillars with long-term strengthand enough size to support the stiff roof during mining activities.Based on the miningconditions of Baixiang wollastonite mine in Changxing County of Zhejiang,while consideringpillars with different shape,irregular size,and distribution,the load imposed on the pillarswas analyzed,and the safety coefficient was calculated in order to determine theirsupport status.The strength of stiff roof was calculated by means of analytical solution-theory of rectangle thin plate rested on elastic foundation.The system stability ofpillar and stiff roof was analyzed according to the proportion of the total cross section areaof pillars to the stiff roof area above the mined area.展开更多
Time-fractional diffusion equations are of great interest and importance on describing the power law decay for diffusion in porous media. In this paper, to identify the diffusion rate, i.e., the heterogeneity of mediu...Time-fractional diffusion equations are of great interest and importance on describing the power law decay for diffusion in porous media. In this paper, to identify the diffusion rate, i.e., the heterogeneity of medium, the authors consider an inverse coefficient problem utilizing finite measurements and obtain a local Hlder type conditional stability based upon two Carleman estimates for the corresponding differential equations of integer orders.展开更多
The initial-boundary value problem of an anisotropic porous medium equation■is studied.Compared with the usual porous medium equation,there are two different characteristics in this equation.One lies in its anisotrop...The initial-boundary value problem of an anisotropic porous medium equation■is studied.Compared with the usual porous medium equation,there are two different characteristics in this equation.One lies in its anisotropic property,another one is that there is a nonnegative variable diffusion coefficient a(x,t)additionally.Since a(x,t)may be degenerate on the parabolic boundary∂Ω×(0,T),instead of the boundedness of the gradient|∇u|for the usual porous medium,we can only show that∇u∈L^(∞)(0,T;L^(2)_(loc)(Ω)).Based on this property,the partial boundary value conditions matching up with the anisotropic porous medium equation are discovered and two stability theorems of weak solutions can be proved naturally.展开更多
文摘Based on the open stope method,the stability of the gob area was decided bypillars and stiff roof.Therefore,it was dispensable to leave pillars with long-term strengthand enough size to support the stiff roof during mining activities.Based on the miningconditions of Baixiang wollastonite mine in Changxing County of Zhejiang,while consideringpillars with different shape,irregular size,and distribution,the load imposed on the pillarswas analyzed,and the safety coefficient was calculated in order to determine theirsupport status.The strength of stiff roof was calculated by means of analytical solution-theory of rectangle thin plate rested on elastic foundation.The system stability ofpillar and stiff roof was analyzed according to the proportion of the total cross section areaof pillars to the stiff roof area above the mined area.
基金supported by the National Natural Science Foundation of China(No.11101093)Shanghai Science and Technology Commission(Nos.11ZR1402800,11PJ1400800)
文摘Time-fractional diffusion equations are of great interest and importance on describing the power law decay for diffusion in porous media. In this paper, to identify the diffusion rate, i.e., the heterogeneity of medium, the authors consider an inverse coefficient problem utilizing finite measurements and obtain a local Hlder type conditional stability based upon two Carleman estimates for the corresponding differential equations of integer orders.
基金supported by Natural Science Foundation of Fujian Province(No.2022J011242),China。
文摘The initial-boundary value problem of an anisotropic porous medium equation■is studied.Compared with the usual porous medium equation,there are two different characteristics in this equation.One lies in its anisotropic property,another one is that there is a nonnegative variable diffusion coefficient a(x,t)additionally.Since a(x,t)may be degenerate on the parabolic boundary∂Ω×(0,T),instead of the boundedness of the gradient|∇u|for the usual porous medium,we can only show that∇u∈L^(∞)(0,T;L^(2)_(loc)(Ω)).Based on this property,the partial boundary value conditions matching up with the anisotropic porous medium equation are discovered and two stability theorems of weak solutions can be proved naturally.
