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Stability and regularization of a backward parabolic PDE with variable coefficients
Lanzhou University.
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2281-856X
Lanzhou University.
2010 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 18, 217-243 p.Article in journal (Refereed) Published
Abstract [en]

We consider a backward parabolic partial differential equation (BPPDE) withvariable coefficient a.x; t / in time. A new modification is used on the logarithmic convexitymethod to obtain a conditional stability estimate. Based on a formal solution, wereveal the essence of the ill-posedness and propose a simple regularization method. Moreover,we apply the regularization method to two representative cases. The results of boththeoretical and numerical performance show the validity of our method.

Place, publisher, year, edition, pages
2010. Vol. 18, 217-243 p.
Keyword [en]
Backward parabolic PDE, regularization, variable coefficient, stability, finite difference method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-63346DOI: 10.1515/JIIP.2010.008OAI: oai:DiVA.org:liu-63346DiVA: diva2:378747
Available from: 2010-12-16 Created: 2010-12-16 Last updated: 2013-08-30

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Eldén, Lars

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