Well-posedness and Tikhonov regularization of an inverse source problem for a parabolic equation with an integral constraint

• Published in: Journal of inverse and ill-posed problems Vol. 32; no. 5; pp. 903 - 925
• Main Author: Ngoma, Sedar
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 01.10.2024; Walter de Gruyter GmbH
• Subjects: 35K20; 35R30; 65M32; 65R32; Algorithms; Boundary conditions; Constraints; integral constraint; Inverse problems; Inverse source problem; Morozov discrepancy principle; Parabolic differential equations; parabolic equation; Partial differential equations; Regularity; Regularization; Tikhonov regularization; Well posed problems

We investigate a time-dependent inverse source problem for a parabolic partial differential equation with an integral constraint and subject to Neumann boundary conditions in a domain of , . We prove the well-posedness as well as higher regularity of solutions in Hölder spaces. We then develop and i...