含有非线性梯度项的退化抛物方程解的爆破率估计  

Blow-up Rate Estimate for Degenerate Parabolic Equation With Nonlinear Gradient Term

作　　者：张正策[1] 王彪[1] 

机构地区：[1]西安交通大学理学院,西安710049

出　　处：《应用数学和力学》2010年第6期756-764,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金青年资助项目(10701061)

摘　　要：利用尺度变换方法和抛物方程的正则性估计,证明了一类含有非线性梯度项的退化多孔介质方程解的爆破率,它是由扩散项和边界流相互作用决定的.与以前有关的结论比较,有趣的发现是,次数不超过2的梯度项不会影响解的爆破率.Blow-up rate was obtained for a porous medium equation with nonlinear gradient term and a nonlinear boundary flux. By using the scaling method and the regularity estimates of parabolic equations, the blow-up rate which was determined by the interaction between the diffusion and the boundary flux was gotten. Interestingly, compared with the previous results, the gradient term which exponent does not exceed 2 will not affect the blow-up rate for solutions.

关 键 词：退化抛物方程 梯度 爆破 非线性边界流 

分 类 号：O175.26[理学—数学] O175.29[理学—基础数学]