The Bernstein estimates of viscosity solutions of linear parabolic equations

1995 ◽  
Vol 11 (3) ◽  
pp. 255-262
Author(s):  
Yi Zhan
Keyword(s):  
Viscosity Solutions ◽  
Parabolic Equations ◽  
Linear Parabolic Equations

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.

Identifications of parameters in ill-posed linear parabolic equations

2004 ◽  
Vol 57 (5-6) ◽  
pp. 677-686 ◽  
Author(s):  
Chaohua Jia ◽  
Gengsheng Wang
Keyword(s):  
Parabolic Equations ◽  
Linear Parabolic Equations ◽  
Ill Posed
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