Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators. (1st December 2022)

• Record Type: Journal Article
• Authors: Slodička, Marian
• Is Part Of: Inverse problems. Volume 38:Number 12(2022)
• Publication Date: 2022-12-01
• Subjects: direct and inverse source problem -- Volterra operator -- variable order time-fractional derivative; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac95bb
• Languages: English
• ISSNs: 0266-5611

Abstract

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.