Lakhdari, A. and Boussetila, N. (2015) An Iterative Regularization Method for an Abstract Ill-Posed Biparabolic Problem. Boundary Value Problems, 55, 1-17.
http://dx.doi.org/10.1186/s13661-015-0318-4

has been cited by the following article:

• TITLE: Stability and Regularization Method for Inverse Initial Value Problem of Biparabolic Equation

  AUTHORS: Hongwu Zhang, Xiaoju Zhang

  KEYWORDS: Inverse Initial Value Problem, Biparabolic Equation, Conditional Stability, Regularization Method, Convergence Estimate

  JOURNAL NAME: Open Access Library Journal, Vol.2 No.5, May 14, 2015

  ABSTRACT: We consider an inverse initial value problem of the biparabolic equation; this problem is ill-posed and the regularization methods are needed to stabilize the numerical computations. This paper firstly establishes a conditional stability of Holder type, then uses a modified regularization method to overcome its ill-posedness and gives the convergence estimate under an a-priori assumption for the exact solution. Finally, a numerical example is presented to show that this method works well.