Recovering Initial States in Semilinear Parabolic Problems from Time-Averages
arXiv:2407.03829
Abstract
Well-posedness of certain semilinear parabolic problems with nonlocal initial conditions is shown in time-weighted spaces. The result is applied to recover the initial states in semilinear parabolic problems with nonlinearities of superlinear behavior near zero from small time-averages over arbitrary time periods.
19 pages