Flat fronts and stability for the porous medium equation
Flat fronts and stability for the porous medium equation
复制标题
多孔介质方程的平坦前沿和稳定性
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Clemens Kienzler
中科院分区：
文献类型：
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作者：
Clemens Kienzler
本文研究了多孔介质方程∂tρ = Δxρm, m > 1。它显示了在齐次Lipschitz意义下接近平坦行波前的解的压力的稳定性，这在某种程度上是最适合处理方程的。这是这种类型的第一个结果，并意味着对压力的任意数量的导数的全局正则性估计。结果包括平滑性，时间和切线方向的分析性，以及空区域和占用区域之间界面的分析性。
ABSTRACT This work is concerned with the equation ∂tρ = Δxρm, m > 1, known as the porous medium equation. It shows stability of the pressure of solutions close to flat travelling wave fronts in the homogeneous Lipschitz sense that is in a way optimal for the treatment of the equation. This is the first result of this type and implies global regularity estimates for any number of derivatives of the pressure. Consequences include smoothness, analyticity in temporal and tangential directions, and analyticity of the interface between empty and occupied regions.