Carleman weight functions for solving ill-posed Cauchy problems for quasilinear PDEs. (6th November 2015)

• Record Type: Journal Article
• Authors: Klibanov, Michael V
• Is Part Of: Inverse problems. Volume 31:Number 12(2015:Dec.)
• Publication Date: 2015-11-06
• Subjects: Carleman estimates -- Ill-Posed Cauchy problems -- semilinear PDEs; 35R30; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/12/125007
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This is the first publication in which a numerical method with rigorously guaranteed convergence is presented for some ill-posed Cauchy problems for semilinear PDEs of the second order. The key tool is the use of the Carleman weight functions in a Tikhonov-like functionals. The method works for elliptic, parabolic and hyperbolic semilinear equations of the second order.