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Seminar No.1794 On mathematical models by (variable-order) time-fractional diffusion equations

Created Date 4/15/2019 福平   View Numbers  56 Return    
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Title: On mathematical models by (variable-order) time-fractional diffusion equations
Reporter: Prof. Hong Wang (Department of Mathematics, University of South Carolina)
Time: 2019-5-13 (Monday) 14:00
Place: G507

Abstract: Recently, Stynes et al proved that time-fractional diffusion equations (tFDEs) generate solutions with singularity near the initial time t=0, which makes the error estimates in the literature that were proved under full regularity assumptions of the true solutions inappropriate.From a modeling point of view, the singularities of the solutions to tFDEs at t=0 do not seem physically relevant to the diffusive transport the tFDEs model. The fundamental reason lies between the incompatibility between the nonlocality of tFDEs and the locality of the initial condition.To eliminate the incompatibility, we propose a modified tFDE model in which the fractional order will vary near the time t=0, which naturally leads to variable-order tFDEs. We will also show that variable-order tFDEs occur naturally in applications. Finally, we briefly discuss the mathematical difficulties in the analysis of variable-order tFDEs, since many widely used Laplace transform based techniques do not apply here.

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