Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators. (1st December 2022) - Slodička, Marian
Abstract: This paper deals with direct and inverse source problems for parabolic or byperbolic PDEs containing nonlinear Volterra operators (including the variable order time-fractional derivatives ). We show the well posedness (existence and uniqueness of a solution) of various settings. The proof-technique is based on the contraction mapping theorem and on a bootstrap argument, which ensures the existence of a global in time solution.