Global Existence for Heat Equation with Nonlinear and Damping Piecewise Neumann Boundary Condition

The Columbia space shuttle catastrophe in 2003 served as the inspiration for this paper’s improved mathematical model, which includes a nonlin-ear 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 pro-vide strong mathematical arguments for the existence of solutions both lo-cally 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.