Tesis
THESIS DEFENSE -- Some results in diffusive partial differential equations
Ponente: Joaquín Domínguez de Tena ()Director/es: José María Arrieta (ICMAT-UCM), Aníbal Rodríguez Bernal (ICMAT-UCM)Fecha: lunes 03 de noviembre de 2025 - 11:00Lugar: B14, Facultad de Matemáticas, Universidad Complutense de Madrid
Resumen:
Diffusion equations play a central role in many areas of science, including physics, biology, and economics, and arise naturally in various branches of mathematics such as partial differential equations and probability theory. Their analysis raises several fundamental mathematical questions, including the existence and uniqueness of solutions, their regularity, global behaviour, asymptotic properties, and dependence on the domain and parameters.
During my PhD, I have investigated several of these aspects in different settings. The thesis is divided into three independent chapters. The first chapter studies the asymptotic behaviour of solutions to the heat equation in exterior domains. The second addresses the Neumann problem for diffusive Hamilton–Jacobi equations. The final chapter focuses on a diffusion problem that combines homogenization theory, thin domains, and graph structures.
