Abstract:
In this study, nonlinear heat equations in a semi-infinite domain are thoroughly investigated, focusing on their solvability and behavior within a significant mathematical framework. By employing the Galerkin method and demonstrating convergence properties in function spaces, the research confirms the existence and accuracy of solutions to these equations. The thesis contributes to understanding heat transfer phenomena and mathematical modeling of complex systems through a detailed examination of theoretical background, problem statement, and objectives. Utilizing advanced mathematical techniques like the Galerkin method, we establish both the existence and uniqueness of solutions to the nonlinear heat equation in a semi-infinite domain. Rigorous analysis validate the stability properties of these solutions, providing insights into heat conduction in materials and the behavior of heat transfer in nonlinear systems. This work enriches knowledge in mathematical modeling and heat transfer phenomena, offering valuable insights for further exploration and applications in scientific and engineering domains.
