Control & Stabilization
Boundary and internal control mechanisms for dispersive PDEs, including KP, KdV–KdV, and related systems.
Applied mathematics · PDEs · Control theory
Juan Ricardo
Muñoz
Postdoctoral Researcher
Universidad de Chile
01 · About
I study how complex systems evolve, stabilize, and can be controlled.
I am a postdoctoral researcher at the Department of Mathematical Engineering, Universidad de Chile, and principal researcher of the FONDECYT 2026 project Control and Long-Time Behavior for Dispersive Equations, supervised by Prof. Claudio Muñoz.
My work lies at the intersection of partial differential equations, control theory, numerical analysis, and scientific machine learning—with particular interest in dispersive models, Lyapunov equations, and reduced-order methods.
02 · Research
Research directions
Analytical foundations meet computational methods.
Long-Time Dynamics
Energy decay, asymptotic behavior, critical domains, and time-delay effects in nonlinear evolution equations.
Operator Equations
Spectral properties and Schatten-class estimates for Lyapunov Gramians in infinite-dimensional control systems.
Scientific Machine Learning
Reduced-order models and neural surrogates for parametric optimal control and PDE-constrained optimization.
“Find what you love and let it kill you.”
— Charles Bukowski
03 · Publications
Selected work
ORCID profile ↗Journal articles
2026Schatten Norm Estimates for Lyapunov Gramians in Operator ScalesL. Grubišić, M. Lazar & J. R. MuñozApplied Mathematics Letters 179, 109968↗ 2025Boundary Exponential Stabilization for the Linear KP-II Equation without Critical Size RestrictionsF. A. Gallego & J. R. MuñozJournal of Dynamical and Control Systems 31, 14↗ 2024On the Boundary Stabilization of the KdV–KdV System with Time-Dependent DelayR. A. Capistrano-Filho, B. Chentouf, V. H. Gonzalez Martinez & J. R. MuñozNonlinear Analysis: Real World Applications 79, 104122↗ 2023Stabilization of the Kawahara–Kadomtsev–Petviashvili Equation with Time-Delayed FeedbackR. A. Capistrano-Filho, V. H. Gonzalez Martinez & J. R. MuñozProceedings of the Royal Society of Edinburgh Section A 155, 260–306↗Preprints
Submitted
Overcoming Slow Kolmogorov Width Decay in Parametric Optimal Control via Neural Network Surrogates
H. Kleikamp, M. Lazar & J. R. Muñoz
↗arXiv:2409.03221Critical Lengths for the Linear Kadomtsev–Petviashvili Equation
R. A. Capistrano-Filho, F. A. Gallego & J. R. Muñoz
↗arXiv:2408.15705Exponential Stabilization for the Hirota–Satsuma System by Boundary Time-Delay Input
V. H. Gonzalez Martinez & J. R. Muñoz
↗“Research is what I’m doing when I don’t know what I’m doing.”
— Wernher von Braun
04 · Curriculum
Academic path
Colombia · Brazil · Croatia · Chile
Detailed CV ↗Postdoctoral Researcher
Universidad de ChileFONDECYT: Control and Long-Time Behavior for Dispersive Equations
Postdoctoral Researcher
University of DubrovnikApplied Mathematics · CONDUCTION project
Ph.D. in Mathematics
Universidade Federal de PernambucoControl and stabilization of KdV–KdV and KP-type systems
M.Sc. in Mathematics
Universidade Federal de PernambucoWell-posedness and control for a KdV–KdV model
B.S. in Mathematics
Universidad Nacional de ColombiaDissipation and regularizing effects for the Boussinesq system
“And once the storm is over, you won’t remember how you made it through, how you managed to survive. You won’t even be sure whether the storm is really over. But one thing is certain. When you come out of the storm, you won’t be the same person who walked in. That’s what this storm’s all about.”
— Haruki Murakami, Kafka on the Shore
05 · Teaching & Agenda
Teaching
Ordinary Differential Equations
Universidad de Chile
Introduction to Calculus
Universidad de Chile
Agenda
2026
VII Colóquio de Matemática da Região Nordeste
Federal University of Pernambuco · Recife, Brazil
InterCoML Conference: NextGen Synergy
Czech University of Life Sciences · Prague, Czech Republic
Short-Term Scientific Mission to IDea_Lab
University of Graz · Graz, Austria
CONDUCTION · Third Project Meeting
Dubrovnik, Croatia
Research Workshop on Validated Methods in Scientific Machine Learning
University of Zagreb · Zagreb, Croatia
2025
8th Najman Conference on Spectral Theory and Differential Equations
Dubrovnik, Croatia
Scientific visit to Prof. Fernando Gallego
Universidad Nacional de Colombia · Manizales, Colombia
School of Analysis and PDEs
Manizales, Colombia
EECI School: Control and Machine Learning
Dubrovnik, Croatia
Summer School: Control, Inverse Problems and Spectral Theory
Toulouse, France
CONDUCTION · Second Project Meeting
Dubrovnik, Croatia
“The world is an illusion, and living is dreaming, it read: How is that dream so vivid? How does blood flow and hot tears gush forth?”
— Han Kang, Greek Lessons