scholarly journals Truncated spectral regularization for an ill-posed non-linear parabolic problem

2019 ◽  
Vol 69 (2) ◽  
pp. 545-569
Author(s):  
Ajoy Jana ◽  
M. Thamban Nair
Keyword(s):  
Parabolic Problem ◽  
Spectral Regularization ◽  
Linear Parabolic Problem ◽  
Non Linear ◽  
Ill Posed

scholarly journals Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

2005 ◽  
Vol 2005 (4) ◽  
pp. 523-536
Author(s):  
Yubin Yan
Keyword(s):  
Difference Method ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Approximation Scheme ◽  
Time Derivative ◽  
Nonsmooth Data ◽  
Smoothing Property ◽  
Linear Parabolic Equations ◽  
Linear Parabolic Problem ◽  
Data Error

A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for the approximation of time derivative has been obtained.

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