The Truncation Regularization Method for Identifying the Initial Value on Non-Homogeneous Time-Fractional Diffusion-Wave Equations

Fan Yang, Qu Pu, Xiao-Xiao Li and Dun-Gang Li
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Fan Yang: Department of Applied Mathematics, School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
Qu Pu: Department of Applied Mathematics, School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
Xiao-Xiao Li: Department of Applied Mathematics, School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
Dun-Gang Li: Department of Applied Mathematics, School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Mathematics, 2019, vol. 7, issue 11, 1-21

Abstract: In the essay, we consider an initial value question for a mixed initial-boundary value of time-fractional diffusion-wave equations. This matter is an ill-posed problem; the solution relies discontinuously on the measured information. The truncation regularization technique is used for restoring the initial value functions. The convergence estimations are given in a priori regularization parameter choice regulations and a posteriori regularization parameter choice regulations. Numerical examples are given to demonstrate this is effective and practicable.

Keywords: time-fractional wave-diffusion equation; identify initial value; truncation regularization method; ill-posed problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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