Uniqueness for an inverse source problem of determining a space dependent source in a non-autonomous parabolic equation. (September 2020)

• Record Type: Journal Article
• Authors: Slodička, Marián
• Is Part Of: Applied mathematics letters. Volume 107(2020)
• Publication Date: 2020-09
• Subjects: Parabolic equation -- Inverse source problem -- Uniqueness; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106395
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We study uniqueness for an inverse source problem for a second order parabolic equation ∂ t u ( x, t ) + A ( t ) u ( x, t ) = h ( t ) f ( x ) with time dependent coefficients. The unknown space dependent source f ( x ) is determined from the final time overdetermination. New uniqueness results are formulated in Theorems 2.1 and 3.1, assuming 0 ⁄ ≡ h ≥ 0 .