![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
Abstract
The left-boundary data of temperature and heat flux are used to estimate an unknown heat conductivity function in a nonlinear heat conduction equation. A Lie-group adaptive method (LGAM) is developed to derive a Lie-group equation defined at two different times, which can be used to recover a spatial-dependence heat conductivity function through a few iterations. Also, the one-dimensional Calderón inverse problem is addressed by applying the present methodology to recover a steady-state heat conductivity coefficient in terms of space variable. The convergence speed and accuracy of the present LGAM are examined by linear and nonlinear numerical examples under noisy input data.
Acknowledgments
It is acknowledged that the author has been promoted as being a Lifetime Distinguished Professor of National Taiwan University. Taiwan's National Science Council project NSC-102-2221-E-002-125-MY3 and the 2011 Outstanding Research Award, as well as the 2011 Taiwan Research Front Award from Thomson Reuters granted to the author, are highly appreciated.