Perturbation of analytic semigroups in scales of Banach spaces and applications to linear parabolic equations with low regularity data

SeMA Journal ◽  
2011 ◽  
Vol 53 (1) ◽  
pp. 3-54 ◽  
Author(s):  
A. Rodríguez-Bernal
Keyword(s):  
Banach Spaces ◽  
Parabolic Equations ◽  
Analytic Semigroups ◽  
Low Regularity ◽  
Linear Parabolic Equations ◽  
Scales Of Banach Spaces

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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