Weak solution to a Robin problem of anomalous diffusion equations: Uniqueness and stable algorithm for the TPC system. (7th October 2022)

• Record Type: Journal Article
• Authors: Xu, Dinghua; Peng, Peng
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 4(2023)
• Page Start: 4587
• Page End: 4601
• Publication Date: 2022-10-07
• Subjects: fractional diffusion equations -- fractional Robin boundary condition -- Riemann‐Liouville fractional derivative -- stable difference scheme -- variational formulation -- weak solutions; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8783
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : A Riemann‐Liouville fractional Robin boundary‐value problem is proposed to describe the fast heat transfer law both within isotropic materials and through the boundary of the materials in high temperature environment. The variational formulation of the fractional model is derived, and further, the energy estimation of the weak solution is deduced. Subsequently, the uniqueness theorem of weak solution is proved. A valid and stable finite difference scheme is developed for the fractional model. The numerical experiments are implemented to indicate that the fractional model is applicable to discover the thermal superdiffusion in the thermal protective clothing (TPC) system and numerical algorithms are effective to improve the intelligence of TPC design.