One-Dimensional Parabolic Equations

2009 ◽  
pp. 327-417
Keyword(s):  
Parabolic Equations ◽  
One Dimensional

The backward problem of parabolic equations with the measurements on a discrete set

2020 ◽  
Vol 28 (1) ◽  
pp. 137-144 ◽  
Author(s):  
Jin Cheng ◽  
Yufei Ke ◽  
Ting Wei
Keyword(s):  
Parabolic Equations ◽  
Numerical Approximation ◽  
Cross Validation ◽  
Continuation Method ◽  
Measurement Data ◽  
Initial Value ◽  
One Dimensional ◽  
Backward Problem ◽  
The One ◽  
Validation Rule

AbstractThe backward problems of parabolic equations are of interest in the study of both mathematics and engineering. In this paper, we consider a backward problem for the one-dimensional heat conduction equation with the measurements on a discrete set. The uniqueness for recovering the initial value is proved by the analytic continuation method. We discretize this inverse problem by a finite element method to deduce a severely ill-conditioned linear system of algebra equations. In order to overcome the ill-posedness, we apply the discrete Tikhonov regularization with the generalized cross validation rule to obtain a stable numerical approximation to the initial value. Numerical results for three examples are provided to show the effect of the measurement data.

scholarly journals Reachability Analysis for One Dimensional Linear Parabolic Equations

2018 ◽  
Vol 51 (16) ◽  
pp. 133-138 ◽  
Author(s):  
Hoang-Dung Tran ◽  
Weiming Xiang ◽  
Stanley Bak ◽  
Taylor T. Johnson
Keyword(s):  
Parabolic Equations ◽  
Reachability Analysis ◽  
One Dimensional ◽  
Linear Parabolic Equations
Sign in / Sign up

Export Citation Format

Share Document