The final value problem for anomalous diffusion equations involving weak-valued nonlinearities

We are concerned with the final value problem governed by a class of semilinear anomalous diffusion equations, where the nonlinearity may take values in Hilbert scales with negative orders. The solvability and Holder regularity results are proved by establishing estimates in Hilbert scales for resolvent operators in connection with nonlinearity function. The obtained results are applicable for some concrete problems modeling subdiffusion phenomena. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

We study a class of final value problems governed by semilinear anomalous diffusion equations, where the nonlinearity can take values in Hilbert scales with negative orders. By establishing estimates in Hilbert scales for resolvent operators in connection with nonlinearity function, we prove the solvability and Holder regularity results, which are applicable to some specific problems modeling subdiffusion phenomena.