Global Existence for Heat Equation with Nonlinear and Damping Piecewise Neumann Boundary Condition
(1) * Iqbal M. Batiha Mail (1) Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan. 2) Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates)
(2) Zainouba Chebana Mail (University of Larbi Ben M’hidi, Algeria)
(3) Taki-Eddine Oussaeif Mail (University of Larbi Ben M’hidi, Algeria)
(4) Sana Abu-Ghurra Mail (Applied Science Private University, Jordan)
(5) Abeer Al-Nana Mail (Prince Sattam Bin Abdulaziz University, Saudi Arabia)
(6) Anwar Bataihah Mail (Jadara University, Jordan)
(7) Iqbal H. Jebril Mail (Al Zaytoonah University of Jordan, Jordan)
*corresponding author

Abstract


The Columbia space shuttle catastrophe in 2003 served as the inspiration for this paper’s improved mathematical model, which includes a nonlinear damping Neumann boundary condition. By creating and examining a modified heat equation with piecewise nonlinear source terms and damping Neumann boundary conditions, the study seeks to investigate the incident’s heat transport dynamics. To ensure that the problem is well-posed, we provide strong mathematical arguments for the existence of solutions both locally and globally. In addition, we use numerical simulations to show how the nonlinear boundary conditions affect heat dissipation and to confirm the theoretical results. The findings advance our knowledge of thermal modeling in aircraft applications and offer greater insights into heat propagation under such conditions.

Keywords


Heat Equation; Damping Term; Existence; Nonlinear Boundary Condition

   

DOI

https://doi.org/10.31763/ijrcs.v5i2.1653 		      

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