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Stability and regularization of a backward parabolic PDE with variable coefficients
Lanzhou University.
Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0003-2281-856X
Lanzhou University.
2010 (engelsk)Inngår i: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 18, s. 217-243Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2010. Vol. 18, s. 217-243
Emneord [en]
Backward parabolic PDE, regularization, variable coefficient, stability, finite difference method
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-63346DOI: 10.1515/JIIP.2010.008OAI: oai:DiVA.org:liu-63346DiVA, id: diva2:378747
Tilgjengelig fra: 2010-12-16 Laget: 2010-12-16 Sist oppdatert: 2017-12-11

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