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.