Missing boundary data reconstruction for the heat equation

2021 ◽  
Author(s):  
Amel Ben Abda ◽  
Naima Benmeghnia ◽  
Rim Guetat
Keyword(s):  
Heat Equation ◽  
Boundary Data ◽  
Data Reconstruction

scholarly journals Missing boundary data reconstruction via an approximate optimal control

2008 ◽  
Vol 2 (4) ◽  
pp. 411-426 ◽  
Author(s):  
Rajae Aboulaϊch ◽  
◽  
Amel Ben Abda ◽  
Moez Kallel ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Boundary Data ◽  
Data Reconstruction

scholarly journals The wave, Laplace, and heat equations and related transforms

1970 ◽  
Vol 11 (2) ◽  
pp. 117-125 ◽  
Author(s):  
J. W. Dettman
Keyword(s):  
Harmonic Function ◽  
Heat Equation ◽  
Boundary Data ◽  
Initial Temperature ◽  
Heat Equations ◽  
Time Axis ◽  
Image Position

This paper is concerned with three basic transformsThe first of these has been studied by Widder [1], who points out that f(t) can be interpreted as the temperature u(0, t) on the time axis, where u(x, t) is the solution of the heat equation withsymmetric initial temperature u(x, 0) = g(|x|). The second has also been studied by Widder [2], where it is pointed out that f(t) can be interpreted as the value of the harmonic function u(x, t) on the t-axis arising from the boundary data u(x, 0) = g(|x|).

Missing boundary data reconstruction by the factorization method

2009 ◽  
Vol 347 (9-10) ◽  
pp. 501-504 ◽  
Author(s):  
Amel Ben Abda ◽  
Jacques Henry ◽  
Fadhel Jday
Keyword(s):  
Boundary Data ◽  
Factorization Method ◽  
Data Reconstruction

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

Sign in / Sign up

Export Citation Format

Share Document