Blow-up Rate Estimate for Degenerate Parabolic Equation With Nonlinear Gradient Term
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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.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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Key words:
- degenerate parabolic equation /
- gradient /
- blow-up /
- nonlinear boundary flux
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