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

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