Stability and regularization of a backward parabolic PDE with variable coefficients
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
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.
Backward parabolic PDE, regularization, variable coefficient, stability, finite difference method
IdentifiersURN: urn:nbn:se:liu:diva-63346DOI: 10.1515/JIIP.2010.008OAI: oai:DiVA.org:liu-63346DiVA: diva2:378747