scholarly journals Singular solutions for semi-linear parabolic equations on nonsmooth domains

2007 ◽  
Vol 333 (2) ◽  
pp. 604-613 ◽  
Author(s):  
Lotfi Riahi
Keyword(s):  
Parabolic Equations ◽  
Singular Solutions ◽  
Nonsmooth Domains ◽  
Linear Parabolic Equations

scholarly journals Singularities of Complex-Valued Solutions to Linear Parabolic Equations

2020 ◽  
Author(s):  
Connor Mooney
Keyword(s):  
Parabolic Equations ◽  
Singular Solutions ◽  
Energy Estimates ◽  
Linear Parabolic Equations ◽  
Complex Valued ◽  
Complex Coefficients

Abstract We construct examples of complex-valued singular solutions to linear, uniformly parabolic equations with complex coefficients in dimension $n \geq 2$, which are exactly as irregular as parabolic energy estimates allow.

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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