Weak solution to a Robin problem of anomalous diffusion equations:
uniqueness and stable algorithm for the TPC system
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
given, and further the energy estimation of the weak solution is
deduced. The uniqueness theorem of weak solution is proved. A valid
finite difference scheme is developed for the fractional model and
numerical experiment is implemented. Numerical results 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.