On a dynamic boundary condition for singular degenerate parabolic equations in a half space
On a dynamic boundary condition for singular degenerate parabolic equations in a half space
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半空间奇异简并抛物线方程的动态边界条件
DOI：
10.1007/s00030-018-0542-6
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Nao Hamamuki
中科院分区：
文献类型：
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作者：
Yoshikazu Giga;Nao Hamamuki
研究半空间中一类具动力边界条件的完全非线性退化抛物型方程的初值问题。我们的设置包括几何方程的奇异性，如水平集平均曲率流方程。建立了粘性上下解的比较原理。我们还证明了解的存在性和唯一解的Lipschitz正则性。此外，与其他类型的边界条件的关系进行了研究，通过研究的渐近行为的解关于系数的动态边界条件。
We consider the initial value problem for a fully-nonlinear degenerate parabolic equation with a dynamic boundary condition in a half space. Our setting includes geometric equations with singularity such as the level-set mean curvature flow equation. We establish a comparison principle for a viscosity sub- and supersolution. We also prove existence of solutions and Lipschitz regularity of the unique solution. Moreover, relation to other types of boundary conditions is investigated by studying the asymptotic behavior of the solution with respect to a coefficient of the dynamic boundary condition.