Dynamical Systems of Partial Differential Equations

This course introduces the theory of dynamical systems governed by partial differential equations, with emphasis on modeling, existence, blow-up phenomena, and stability analysis.
It covers local and global existence of PDE systems, as well as local and global stability using eigenvalue analysis and Lyapunov methods.
The course also examines diffusion-driven instability and bifurcation phenomena in PDE models.
Applications from physics and applied sciences are used to illustrate the theoretical concepts.