Very singular diffusion equations: second and fourth order problems
Very singular diffusion equations: second and fourth order problems
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DOI：
10.1007/s13160-010-0020-y
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发表时间：
2010-05
影响因子：
0.9
通讯作者：
M. Giga;Y. Giga
中科院分区：
文献类型：
--
作者：
M. Giga;Y. Giga
本文研究了扩散效应强到演化速度成为非局部量的奇异扩散方程。典型的例子包括总变分流和二级结晶流。本文包含了与二阶模型相比研究较少的四阶模型。该模型的典型例子是全变分的h−1梯度流。结果表明，这种流与二阶全变分流有很大的不同。例如，我们通过一个显式的例子证明，对于四阶全变分流，解可以瞬间发展为跳变不连续。
This paper studies singular diffusion equations whose diffusion effect is so strong that the speed of evolution becomes a nonlocal quantity. Typical examples include the total variation flow as well as crystalline flow which are formally of second order. This paper includes fourth order models which are less studied compared with second order models. A typical example of this model is anH−1gradient flow of total variation. It turns out that such a flow is quite different from the second order total variation flow. For example, we prove by giving an explicit example that the solution may instantaneously develop a jump discontinuity for the fourth order total variation flow.