4 papers
Random domain decomposition for parabolic PDEs on graphs
Martín Hernández
The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require consider…
Random Batch Methods for Discretized PDEs on Graphs
Martín Hernández, Enrique Zuazua
Gas transport and other complex real-world challenges often require solving and controlling partial differential equations (PDEs) defined on graph structures, which typically deman…
Averaged observations and turnpike phenomenon for parameter-dependent systems
Martín Hernández, Martin Lazar, Sebastián Zamorano
Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations i…
Uniform Turnpike Property and Singular Limits
Martin Hernandez, Enrique Zuazua
Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform w…