Resolução de equações de difusão em domínios infinitos, semi-infinitos e limitados: métodos matemáticos e aplicações

Abstract

This dissertation presents a detailed and comprehensive analysis of the methodologies used to solve problems involving the diffusion equation, which is fundamental for describing transport processes in various fields such as physics, chemistry, biology, engineering, and finance, making a deep understanding of its solutions essential. The purpose of this study is to serve as a compendium, a reference guide intended for both beginning students and professionals who use the diffusion equation in their research and practice. It offers a clear and structured introduction to the diffusion equation and its various solutions, with detailed examples and explanations. Thus, students can develop a solid understanding of the theoretical concepts, and for professionals already working in the field, it serves as a reference guide, compiling a variety of analytical methods. This work can become a valuable tool for both the academic community and professional practice, as it facilitates learning, application, and continuous research on the diffusion equation, significantly contributing to the advancement of knowledge by promoting a connection between theory and practice, which is essential for the development of innovative and effective solutions.