A kinetic approach to comparison properties for degenerate parabolic-hyperbolic equations with boundary conditions
A kinetic approach to comparison properties for degenerate parabolic-hyperbolic equations with boundary conditions
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DOI：
10.1016/j.jde.2006.07.008
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发表时间：
2006-11
影响因子：
2.4
通讯作者：
Kazuo Kobayasi
中科院分区：
文献类型：
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作者：
Kazuo Kobayasi
我们研究具有初始和非齐次边界条件的简并抛物线-双曲方程的比较原理。我们证明了任何熵子解和超解的比较定理。迄今为止，一些作者已经获得了 L1 收缩性以及熵解的唯一性，但似乎任何比较定理都尚未得到证明。这里使用的方法是克鲁兹科夫提出的加倍变量技术。我们的方法基于动力学公式和动力学技术。通过开发具有边界条件的简并抛物双曲方程的动力学技术，我们可以获得明显扩展 L1 收缩性质的比较性质。
We study the comparison principle for degenerate parabolic–hyperbolic equations with initial and nonhomogeneous boundary conditions. We prove a comparison theorem for any entropy sub- and supersolution. The L1contractivity and, therefore, uniqueness of entropy solutions has been obtained so far by some authors, but it seems that any comparison theorem is not proven. The method used there is the doubling variable technique due to Kružkov. Our method is based upon the kinetic formulation and the kinetic techniques. By developing the kinetic techniques for degenerate parabolic–hyperbolic equations with boundary conditions, we can obtain a comparison property which obviously extends the L1contractive property.