Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order
Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order
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DOI：
10.1051/m2an/2020072
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发表时间：
2020-10
期刊：
影响因子：
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通讯作者：
Buyang Li;Hong Wang;Jilu Wang
中科院分区：
文献类型：
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作者：
Buyang Li;Hong Wang;Jilu Wang
我们证明了具有可变分数阶的分数扩散多孔介质方程解的适定性和正则性。提出了一种线性隐式时间步进方法，在时间上对方程进行线性化和离散化，并根据证明的正则性结果对数值解的收敛性进行了严格的分析。
We prove well-posedness and regularity of solutions to a fractional diffusion porous media equation with a variable fractional order that may depend on the unknown solution. We present a linearly implicit time-stepping method to linearize and discretize the equation in time, and present rigorous analysis for the convergence of numerical solutions based on proved regularity results.