loading page

On the Stefan Problem With Nonlinear Thermal Conductivity
  • Lazhar Bougoffa,
  • Ammar Khanfer
Lazhar Bougoffa
Imam Muhammad bin Saud Islamic University

Corresponding Author:[email protected]

Author Profile
Ammar Khanfer
Prince Sultan University
Author Profile


The solution is obtained and validated by an existence and uniqueness theorem for the following nonlinear boundary value problem \[ \frac{d}{dx}(1+\delta y+\gamma y^{2})^{n}\frac{dy}{dx}]+2x\frac{dy}{dx}=0,\,\,\,x>0,\,\,y(0)=0,\,\,\,y(\infty)=1, \] which was proposed in 1974 by [1] to represent a Stefan problem with a nonlinear temperature-dependent thermal conductivity on the semi-infinite line (0;1). The modified error function of two parameters $\varphi_{\delta,\gamma}$ is introduced to represent the solution of the problem above, and some properties of the function are established. This generalizes the results obtained in [3, 4].
06 Sep 2021Submitted to Mathematical Methods in the Applied Sciences
07 Sep 2021Submission Checks Completed
07 Sep 2021Assigned to Editor
12 Sep 2021Reviewer(s) Assigned
04 Feb 2022Review(s) Completed, Editorial Evaluation Pending
05 Feb 2022Editorial Decision: Revise Major
09 Feb 20221st Revision Received
10 Feb 2022Submission Checks Completed
10 Feb 2022Assigned to Editor
10 Feb 2022Reviewer(s) Assigned
20 Feb 2022Review(s) Completed, Editorial Evaluation Pending
24 Sep 2022Editorial Decision: Accept