报告主题：Wellposedness and regularity of variable order time fractional diffusion equations
报告人：Xiangcheng Zheng 博士生 （Department of Mathematics, University of South Carolina）
报告时间：2019年5月13日（周一）15：00
报告地点：校本部G507
邀请人：李常品
报告摘要：We prove the wellposedness of a nonlinear variable-order fractional ordinary differential equation and the regularity of its solutions, which is determined by the values of the variable order and its high-order derivatives at time t=0. More precisely, we prove that its solutions have full regularity like its integer-order analogue if the variable order has an integer limit at t=0 or exhibits singular behaviors at t=0 like in the case of the constant-order fractional differential equations if the variable order has a non-integer value at time t=0.
We then extend the developed techniques to prove the wellposedness of a variable-order linear time-fractional diffusion equation in multiple space dimensions and the regularity of its solutions, which depends on the behavior of the variable order at t=0 in the similar manner to that of the fractional ordinary differential equations.
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