Unique continuation property for multi-terms time fractional diffusion equations
Unique continuation property for multi-terms time fractional diffusion equations
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DOI：
10.1007/s00208-018-1710-z
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发表时间：
2017-10
影响因子：
1.4
通讯作者：
C. Lin;G. Nakamura
中科院分区：
文献类型：
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作者：
C. Lin;G. Nakamura
本文研究了一类多项时间分数阶扩散方程解的唯一连续性的Carleman估计，该方程具有与时间有关的二阶强椭圆算子。利用一个关于时间的线性的特殊Holmgren型变换，利用伪微分算子的演算，通过对与该变换方程相关的算子的次椭圆估计，得到了解的局部唯一延续的估计。在此基础上，给出了导出解的全局唯一延拓的新论证。这里全局唯一延拓的含义如下。如果u是多项时间分数扩散方程在时间区间（0，T）上的一个解，并且它是支持的，那么在子域上的一个零集解可以被延拓到。
This paper concens about a Carleman estimate which can give the unique continuation property of solutions for a multi-terms time fractional diffusion equation up to orderwith general time dependent second order strongly elliptic operator for the diffusion. By using a special Holmgren type transformation which is linear with respect to time, the estimate giving a local unique continuation of solutions is derived via some subelliptic estimate for an operator associated to this transformed equation using calculus of pseudo-differential operators. After that we have given a new argument to derive the global unique continuation of solutions. Here the global unique continuation means as follows. If u is a solution of the multi-terms time fractional diffusion equation in a domain over the time interval (0,T) and it is supported on, then a zero set of solution over a subdomain ofcan be continued to.