loading page

Memory kernel reconstruction problems in the integro--differential equation of rigid heat conductor
  • Zhonibek Zhumaev,
  • Durdimurod Durdiev
Zhonibek Zhumaev
Bukhara State University
Author Profile
Durdimurod Durdiev
Bukhara State University
Author Profile

Abstract

The inverse problems of determining the energy-temperature relation α(t) and the heat conduction relation k(t) functions in the one-dimensional integro– differential heat equation are investigated. The direct problem is the initial-boundary problem for this equation. The integral terms have the time convolution form of unknown kernels and direct problem solution. As additional information for solving inverse problems, the solution of the direct problem for x = x0 is given. At the beginning an auxiliary problem, which is equivalent to the original problem is introduced. Then the auxiliary problem is reduced to an equivalent closed system of Volterra-type integral equations with respect to unknown functions. Applying the method of contraction mappings to this system in the continuous class of functions with weighted norms, we prove the main result of the article, which is a global existence and uniqueness theorem of inverse problem solutions.

Peer review status:ACCEPTED

24 Sep 2020Submitted to Mathematical Methods in the Applied Sciences
25 Sep 2020Submission Checks Completed
25 Sep 2020Assigned to Editor
08 Oct 2020Reviewer(s) Assigned
04 Nov 2020Review(s) Completed, Editorial Evaluation Pending
08 Nov 2020Editorial Decision: Revise Major
19 Nov 20201st Revision Received
19 Nov 2020Submission Checks Completed
19 Nov 2020Assigned to Editor
24 Nov 2020Reviewer(s) Assigned
25 Nov 2020Review(s) Completed, Editorial Evaluation Pending
25 Nov 2020Editorial Decision: Accept