2023/02/28 by Nair, M. Thamban, Danumjaya, P.
#26A33 #33E12 #35K05 #35R30 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2303.15455
It is well-known that the backward heat conduction problem of recovering the temperature u(⋅, t) at a time t≥ 0 from the knowledge of the temperature at a later time, namely g:= u(⋅, τ) for τ>t, is ill-posed, in the sense that small error in g can lead to large deviation in u(⋅, t). However, in the case of a time fractional backward heat conduction problem (TFBHCP), the above problem is well-posed for t>0 and ill-posed for t=0. We use this observation to obtain stable approximate solutions for the TFBHCP for t=0, and derive error estimates under suitable source conditions. We shall also provide some numerical examples to illustrate the approximation properties of the regularized solutions.