| 含有非线性梯度项的退化抛物方程解的爆破率估计 |
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| 引用本文： | 张正策,王彪.含有非线性梯度项的退化抛物方程解的爆破率估计[J].应用数学和力学,2010,31(6):756-764. |
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| 作者姓名： | 张正策 王彪 |
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| 作者单位： | 西安交通大学 理学院,西安 710049 |
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| 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．
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| 关 键 词： | 退化抛物方程 梯度 爆破 非线性边界流 |
| 收稿时间： | 1900-01-01 |
Blow-up Rate Estimate for Degenerate Parabolic Equation With Nonlinear Gradient Term |
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| WANG Zheng-ce,WANG Biao.Blow-up Rate Estimate for Degenerate Parabolic Equation With Nonlinear Gradient Term[J].Applied Mathematics and Mechanics,2010,31(6):756-764. |
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| Authors: | WANG Zheng-ce WANG Biao |
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| Institution: | College of Science, Xi'an Jiaotong University, Xi'an 710049, P. R. China |
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| Abstract: | Blow-up rate was obtained for a porous medium equation with non linear gradient term and a non linear boundary flux. By using the scaling method and the regularity estmiates of parabolic equations, the blow-up rate which was deter mined by the interaction between the diffusion and the boundary flux was gotten. Interestingly, compared with the previous results, the gradientterm which exponent does not exceed 2 will not affect the blow-up rate for solutions. |
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