Multi-physics problems, involving coupled phenomena such as fluid mechanics, thermodynamics, and chemistry, are common in science and engineering. These problems often involve distinct governing equations (e.g., Navier–Stokes, elasticity, diffusion) and specialized solvers, making monolithic solutions computationally prohibitive. Domain decomposition (DD) offers an effective strategy by partitioning the domain into […]
Math Enrique Zuazua
7 posts
Introduction The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinction of another. Comprehending the mechanisms governing these systems can yield critical insights for developing strategies in ecological management and biodiversity conservation. In this post, we […]
Author: Martin Gugat, Enrique Zuazua, Aleksey Sikstel, FAU DCN-AvH Code: [HINT] To run the software on your computer, you may have to install additional standard software packages (like cmake and a c++ compiler) and additional libraries (lapack, PETSc). In order to optimize the operation of gas transportation networks, […]
Control of Advection-Diffusion Equations on Networks and Singular Limits By Jon Asier Bárcena-Petisco, Márcio Cavalcante, Giuseppe Maria Coclite, Nicola de Nitti and Enrique Zuazua Introduction In the past few decades, models based on partial differential equations have been very effective in tackling many problems dealing with flows on networks (e.g. […]
Averaged dynamics and control for heat equations with random diffusion By Jon Asier Bárcena Petisco, Enrique Zuazua Background and motivation Let us consider the random heat equation described by the following system: for a domain, a subdomain, a control, the initial configuration and the diffusivity coefficient, which is a positive […]
Inverse Design For Hamilton-Jacobi Equations By Carlos Esteve, Enrique Zuazua In many evolution models, the reconstruction of the initial state given an observation of the system at time represents a major challenge in mathematical modelling. Especially if it involves irreversible processes, where sometimes, different initial conditions can lead the system […]
Flows on Networks By Enrique Zuazua, Nicola de Nitti PDE models on Networks In the last few decades, models based on partial differential equations have been very effective in tackling many applied problems dealing with flows on networks. The areas of application include mainly the study of vehicular traffic, […]