scholarly journals Solvability and Blow-up of Solutions of Semi Linear Parabolic Problem with Integral Condition of Second Type

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Saker Meriem ◽  
Oussaeif Taki-Eddine ◽  
Boumaza Nouri
Keyword(s):  
Parabolic Problem ◽  
Blow Up ◽  
Integral Condition ◽  
Linear Parabolic Problem

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.

scholarly journals A STRONGLY ILL-POSED INTEGRO-DIFFERENTIAL PARABOLIC PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

2013 ◽  
Vol 18 (3) ◽  
pp. 395-414
Author(s):  
Alfredo Lorenzi
Keyword(s):  
Parabolic Problem ◽  
Dirichlet Boundary ◽  
Integral Boundary Conditions ◽  
Integral Condition ◽  
Normal Derivative ◽  
Integral Boundary ◽  
Additional Information ◽  
Ill Posed ◽  
Linear Integral ◽  
Continuous Dependence Results

Via Carleman estimates we prove uniqueness and continuous dependence results for an identification and strongly ill-posed linear integro-differential parabolic problem with the Dirichlet boundary condition, but with no initial condition. The additional information consists in a boundary linear integral condition involving the normal derivative of the temperature on the whole of the lateral boundary of the space-time domain.

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