Identify the Robin coefficient in an inhomogeneous time-fractional diffusion-wave equation

Abstract

This paper is devoted to identifying the Robin coefficient in a one-dimensional inhomogeneous time-fractional diffusion-wave equation from the viewpoint of Bayesian inference approach. The priori modeling is implemented by a Markov Random Field (MRF). A hierarchical Bayesian model is adopted to select regularization parameters automatically. The Markov chain Monte Carlo (MCMC) algorithms are conducted to explore the posterior state space. Three numerical examples are carried out to demonstrate the performance of the proposed method.