关注如下的对流扩散方程u_t=div(|▽_u^m|^(p-2)▽_u^m)+sum from i=1 to N((?)b_i(u^m))/((?)x_i)的初边值问题.若p>1+1/m,通过考虑正则化问题的解u_k,利用Moser迭代技巧,得到了u_k的L~∞模与梯度▽_(u_k)的L^p模的局部有界性.利用...关注如下的对流扩散方程u_t=div(|▽_u^m|^(p-2)▽_u^m)+sum from i=1 to N((?)b_i(u^m))/((?)x_i)的初边值问题.若p>1+1/m,通过考虑正则化问题的解u_k,利用Moser迭代技巧,得到了u_k的L~∞模与梯度▽_(u_k)的L^p模的局部有界性.利用紧致性定理,得到了对流扩散方程本身解的存在性.若p<1+1/m,p>2或者p=1+1/m,利用类似的方法可以得到解的存在性.证明了解的唯一性,同时讨论了正性和熄灭性等解的性质.展开更多
Experiments were conducted to investigate the cooling manner of an ultra-thick hot aluminum alloy plate during multistage quenching. Cooling curves and heat flux curves of different rapid quenching flux varied from 23...Experiments were conducted to investigate the cooling manner of an ultra-thick hot aluminum alloy plate during multistage quenching. Cooling curves and heat flux curves of different rapid quenching flux varied from 23 to 40 L min-1 and were analyzed in detail. In this investigation, cooling process was divided into the following four steps： （Ⅰ） starting step, （Ⅱ） rapid cooling step, （Ⅲ） slow cooling step, and （Ⅳ） stopping step. Based on the curves, the calculation method for surface transfer coefficient was provided, and the effects of coefficient on surface temperature and quenching flux were discussed. Results showed that the transfer coefficient disagreed with heat flux and that it is a nonlinear function of surface temperature. The highest coefficient was observed not in the rapid cooling step with the largest heat flux but in the slow cooling step with lower heat flux. The coefficient increased with surface temperature ranging from 480 to 150℃, and a coefficient peak appeared in the temperature range of 150- 100℃. The coefficient also increased with quenching flux. Finally, a simulation was performed using the finite element method to verify the reliability of the coefficient results, which showed good agreement with the measurement values.展开更多
文摘关注如下的对流扩散方程u_t=div(|▽_u^m|^(p-2)▽_u^m)+sum from i=1 to N((?)b_i(u^m))/((?)x_i)的初边值问题.若p>1+1/m,通过考虑正则化问题的解u_k,利用Moser迭代技巧,得到了u_k的L~∞模与梯度▽_(u_k)的L^p模的局部有界性.利用紧致性定理,得到了对流扩散方程本身解的存在性.若p<1+1/m,p>2或者p=1+1/m,利用类似的方法可以得到解的存在性.证明了解的唯一性,同时讨论了正性和熄灭性等解的性质.
基金supported by the National Basic Research Program of China(Grant No.2012CB619500)the Major State Research Program of China(Grant No.2016YFB0300901)+1 种基金the National Natural Science Foundation of China(Grant No.51375503)the BaGui Scholars Program of China’s Guangxi Zhuang Autonomous Region(Grant No.2013A017)
文摘Experiments were conducted to investigate the cooling manner of an ultra-thick hot aluminum alloy plate during multistage quenching. Cooling curves and heat flux curves of different rapid quenching flux varied from 23 to 40 L min-1 and were analyzed in detail. In this investigation, cooling process was divided into the following four steps： （Ⅰ） starting step, （Ⅱ） rapid cooling step, （Ⅲ） slow cooling step, and （Ⅳ） stopping step. Based on the curves, the calculation method for surface transfer coefficient was provided, and the effects of coefficient on surface temperature and quenching flux were discussed. Results showed that the transfer coefficient disagreed with heat flux and that it is a nonlinear function of surface temperature. The highest coefficient was observed not in the rapid cooling step with the largest heat flux but in the slow cooling step with lower heat flux. The coefficient increased with surface temperature ranging from 480 to 150℃, and a coefficient peak appeared in the temperature range of 150- 100℃. The coefficient also increased with quenching flux. Finally, a simulation was performed using the finite element method to verify the reliability of the coefficient results, which showed good agreement with the measurement values.
