【摘要】 多孔介质方程具有广泛的物理背景,可用于刻画流体流动、热传导等在内的物理过程.首先利用凸方法证明了初值充分大时存在有限时刻爆破的解;再利用极大值原理结合积分估计等得出爆破解的爆破速率估计;最后利用L2方法得出爆破解的爆破时间估计,所得结果与初值和势函数V(x)都有关系.在所研究的方程中将势函数取作V(x)≡1,便得到了最典型的具有源项的多孔介质方程.更多还原

【Abstract】 The porous medium equation has a wide physical background.It could characterize many physical phenomea such as the fluid flow and heat conduction etc.This paper studies the blow-up phenomena for a porous medium equation with potential.The authors firstly prove the existence of solutions which blow up in finite time for large initial by the convex method.Then the authors obtain the estimate for the blow-up rate and blow-up time by using maximum principle and L2 method,respectivly.The results depend on the initial data and potential V(x).Taking V(x) ≡1,one gets usual porous medium equation with source.Therefore,the results obtained in this paper are more general.更多还原