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Partial Differential Equations · Control Theory

RobertoCapistrano-Filho

Associate Professor
Department of Mathematics
Federal University of Pernambuco

I study the analysis and control of partial differential equations, with a focus on well-posedness, controllability, and stabilization in fluid models.

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Professor Roberto Capistrano-Filho

Current position

UFPE, Recife

Curiosities

Academic lineageMathematics Genealogy ProjectCollaboration distanceMy Erdős number is 2

“In a way, mathematics is the only infinite human activity. It is conceivable that humanity could eventually learn everything in physics or biology. But humanity certainly won't ever be able to find out everything in mathematics, because the subject is infinite. Numbers themselves are infinite. That's why mathematics is really my only interest.”

— Paul Erdős
01Projects

Research projectsin progress.

Current grants and international cooperation supporting research in analysis, control, and nonlinear dispersive systems.

Active projects

Current grants & international cooperation

4 active projects

CAPES Global.edu · Rede COONEXA08/2026—12/2030

Tecnologias convergentes para a sustentabilidade, inclusão e cooperação global

Funder · CAPES
CNPq · PQ Level B08/2025—07/2029

Dispersive Systems Applied to Fluid Dynamics: Well-Posedness, Control, and Stability

Funder · CNPq
COFECUB / CAPES01/2024—12/2027

International cooperation connecting research groups in Brazil and France

Funder · CAPES & COFECUB
CNPq / MCTI · Call 10/202312/2023—12/2026

Desigualdades assintóticas, singularidades e controlabilidade para alguns sistemas físicos

Funder · CNPq
View all previous projects6 completed
CNPq · Call 26/2021 · Overseas Fellowships09/2022—04/2024

Initial boundary value problems for dispersive equations and applications to fluid dynamics problems

Funder · CNPq
CNPq · PQ203/2022—07/2025

Initial boundary value problems of dispersive systems and their applications to fluid dynamics

Funder · CNPq
MATH-AmSud01/2021—12/2023

International cooperation in analysis, control, and nonlinear dispersive equations

Funder · CONICYT & CMM · COLCIENCIAS · CAPES · CNRS
Universal CNPq03/2019—02/2022

Asymptotic behavior and control properties for nonlinear dispersive systems

Funder · CNPq
PrInt / CAPES03/2018—12/2022

Internationalization project in mathematics

Funder · CAPES
CNPq · PQ203/2018—02/2021

Boa colocação, controle e estabilização para sistemas dispersivos não lineares

Funder · CNPq

Research groups

Long-term academic communities

Permanent member

Graduate Program in Mathematics at UFPE

11/2015—Current

Research group

Research Group of Nonlinear PDEs

11/2015—Current

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02Research

Mathematics forevolving systems.

My research connects analysis, control, and numerical methods to understand how complex systems behave, respond, and can be guided over time.

01

Well-posedness

Existence, uniqueness, and regularity for initial-boundary value problems governed by dispersive PDEs.

02

Controllability

Boundary and internal control strategies for steering nonlinear systems toward prescribed states.

03

Stabilization

Long-time behavior, observability, and feedback mechanisms for systems arising in fluid dynamics.

04

Numerical analysis

Analytical and computational methods for approximating solutions and exploring the dynamics of nonlinear dispersive systems.

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Research manuscripts

Preprints

10 manuscripts · updated from arXiv

P01Submitted

Nonlinear Schrödinger equation in an exterior domain

R. A. Capistrano-Filho, L. Rosier and B.-Y. Zhang

P02Submitted

Unique continuation for the periodic Benjamin-Bona-Mahony equation

R. A. Capistrano-Filho, V. H. Gonzalez Martinez, and A. C. Nascimento

P03Submitted

Optimal polynomial stabilization of the linearized periodic Whitham-Boussinesq system

R. A. Capistrano-Filho and W. A. Roqueta

P04Submitted

Solitary waves for a higher-order Boussinesq system: Stability and numerical experiments

R. A. Capistrano-Filho, J. R. Quintero, and J. C. Muñoz

View all preprints

Browse by topic

Some works appear in more than one area.

10 preprints

P01Submitted

Nonlinear Schrödinger equation in an exterior domain

Waves & models

R. A. Capistrano-Filho, L. Rosier and B.-Y. Zhang

P02Submitted

Unique continuation for the periodic Benjamin-Bona-Mahony equation

ControlWaves & models

R. A. Capistrano-Filho, V. H. Gonzalez Martinez, and A. C. Nascimento

P03Submitted

Optimal polynomial stabilization of the linearized periodic Whitham-Boussinesq system

StabilizationWaves & models

R. A. Capistrano-Filho and W. A. Roqueta

P04Submitted

Solitary waves for a higher-order Boussinesq system: Stability and numerical experiments

StabilizationWaves & modelsNumerical analysis

R. A. Capistrano-Filho, J. R. Quintero, and J. C. Muñoz

P05Submitted

Unique continuation for fifth-order KP equation and its application to control problems

ControlWaves & models

R. A. Capistrano-Filho and A. C. Nascimento

P06Submitted

A nonhomogeneous boundary-value problem for the nonlinear KdV equation on star graphs

Well-posednessWaves & models

R. A. Capistrano-Filho, H. Parada, and J. S. da Silva

P07Submitted

Long-time dynamics of the Zakharov–Kuznetsov equation

StabilizationWaves & models

R. A. Capistrano-Filho and A. C. Nascimento

P08Submitted

Stabilization of a perturbed quintic defocusing Schrödinger equation in R³: The critical case

Stabilization

P. Braz e Silva, R. A. Capistrano-Filho, J. D. N. Carvalho, and D. dos Santos Ferreira

P09Submitted

Critical lengths for the linear Kadomtsev-Petviashvili equation

ControlWaves & models

R. A. Capistrano-Filho, F. Gallego, and J. R. Muñoz

P10Submitted

Control of the Schrödinger equation in R³: The critical case

Control

P. Braz e Silva, R. A. Capistrano-Filho, J. D. N. Carvalho, and D. dos Santos Ferreira

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Publications

Journal papers

48 peer-reviewed articles · 2012—2027

View all 48 journal papers

Browse by topic

Some works appear in more than one area.

48 papers

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03Agenda

Talks, visits& scientific meetings.

A chronological record of conferences, workshops, research visits, and invited talks since 2014.

2026

5 activities
IV Symposium on Nonlinear Partial Differential Equations – Recife – UFPE – Recife – Brazil (20-23 January)
Scientific visit to Chulkwang Kwak at Ewha Womans University, Seoul – Korea (5-24 May).
International Congress on Differential Equations, Dynamical Systems, and Applied Mathematics – Londrina – Brazil (8-11 June)III Workshop on Control Theory and Partial Differential Equations – Niterói – UFF – Rio de Janeiro – Brazil (19-23 October)VII Colóquio de Matemática da Região Nordeste – UFPE – Recife (23-27 November)
View archive · 2014—2025
202512 activities
Summer School DMat – UFPE (January and February)
I Workshop de Análise e Dinâmica da UFAL – Maceió – Alagoas (21-25 January)
Scientific visit to Prof. Fernando Gallego and participation in the “Escuela de Análisis y Ecuaciones Diferenciales” – Universidad Nacional de Colombia – Manizales (25 April-5 May).IX Encontro de Matemática Pura e Aplicada (IX EMPA) – UEPB – Campina Grande – Brazil (10-13 June)Half-Year Seminar in PDE – UFCG – Campina Grande – Paraíba (03-04 July)Mathematical Congress of the Americas – Miami – USA (21-25 July)Brazil-Mexico Joint Mathematical Meeting – Fortaleza – Ceará – Brazil (8-12 September)XLIV Congresso Nacional de Matemática Aplicada e Computacional – Rio de Janeiro – RJ (15-19 September)XIII Jornada de Matemática da UFPI – Teresina – Piauí (23-26 September)Scientific visit to Tristan Robert at Université de Lorraine, Nancy – France (3-8 October)Scientific visit to Prof. Jérôme Le Rousseau at Université Sorbonne Paris Nord, Paris – France (9-16 October)
Scientific visit to UFCG, Campina Grande, Brazil, 11-12 December.
20246 activities
Scientific Visit to Prof. Chulkwang Kwak – Ewha University – Seoul – South Korea (September)
Recife Meeting on Mathematics – Celebrating the 70th birthday of Vilmos Komornik – Recife – Brazil (August)SIAM Conference on Nonlinear Waves and Coherent Structures – Maryland – USA (June)Workshop de Análise da PPGMat UFPI – Píaui – Brazil (March)II Symposium on Nonlinear Partial Differential Equations – Recife – Brazil (February)III Workshop de Equações Dispersivas na UFMG – Belo Horizonte – Belo Horizonte – Brazil (February)
20238 activities
Scientific Visit to Prof. Fernando Gallego – UNAL – Manizales – Colombia (December)
1st Colombian Workshop in Nonlinear Dispersive Equations (November) – Manizales – Colombia
Scientific visit to CMM – University of Chile – Santiago – Chile (October)
SIAM Southeastern Atlantic Section Annual Meeting – Blacksburg – USA (March)Twelfth Ohio River Analysis Meeting – Cincinnati – USA (March)
Scientific visit to Prof. Bingyu Zhang, University of Cincinnati – USA (March)
I Symposium of Nonlinear Partial Differential Equations at UFPE – Recife – Brazil (February)
Visiting Researcher at Virginia Tech, USA (January to July)
20227 activities
MatFest 2022 – Universidade Federal de Alagoas, Brazil (December)V Workshop on Nonlinear Dispersive Equations (WNDE) – Minas Geral – Brazil (November)
Scientific visit to Prof. David Dos Santos – Université de Larraine, France (November)
Scientific visit to Prof. Vilmos Komornik – Université de Strasbourg, France (October)
V Colóquio de Matemática da Região Sul (August)
ICM (July) – St. Petersburg, Russia
VI Encontro de Matemática Pura e Aplicada – Universidade Estadual da Paraíba (June)
20216 activities
Scientific visit to Prof. Márcio Cavalcante (December) – Universidade Federal de Alagoas, Brazil
Scientific visit to Prof. Vilmos Komornik (November) – Université de Strasbourg, France
Scientific visit to Prof. Fernando Gallego (September) – Universidad Nacional de Colombia – Manizales, Colombia
III Summer School of PMA – Universidade Estadual de Maringá – March
Colóquio da Graduação da UFPE – Online event
I workshop de pesquisadores jovens em análise e EDP – Universidade Federal Fluminense. – Online event (Link youtube)
20202 activities
XIV Semana da Matemática da UFRR – Online event (Link youtube)
Scientific visit to Prof. Márcio Cavalcante (March) – Universidade Federal de Alagoas, Brazil
20195 activities
Scientific visit to Prof. Fernando Gallego (November) – Universidad Nacional de Colombia – Manizales, Colombia.
IV Nonlinear Dispersive Equations (November) – UFRJ – Rio de Janeiro – Brazil1st Joint Meeting Brazil-France in Mathematics (July) – IMPA – Rio de Janeiro – BrazilWorkshop de Verão em EDP’s e Sistemas Dinâmicos (February) – UFPE – Recife – Pernambuco – BrazilICMC Summer Meeting on Differential Equations 2019 Chapter – Properties of the biharmonic nonlinear Schrödinger equation (February) – USP São Carlos – São Pualo – Brazil.
20186 activities
Workshop on Inverse and control problems for physical systems ICoPS (December) 2018, Valparaiso, Chile.Scientific visit to Prof. Fernando Gallego – Congreso Semestral en Análisis y Ecuaciones Diferenciales Parciales (November) Universidad Nacional de Colombia – Manizales, Colombia.International Congress of Mathematicians – Global Results on Control and Stabilization of Fourth Order Nonlinear Schrödinger Equation on the Torus (August) – Rio de Janeiro – Rio de Janeiro – Brazil.Nonlinear Dispersive Equations – Global Results on Control and Stabilization of Fourth Order Nonlinear Schrödinger Equation on a Periodic Domain (July) – Florianópolis – Santa Catarina – Brazil.
Participation as a member of the committee of public service exam – UFAL (May) – Maceió -Alagoas – Brazil.
Scientific Visit to Prof. Luiz Gustavo Farah (UFMG) and Segundo Workshop em Equações Dispersivas da UFMG – Critical Length Phenomenon For a Class of Dispersive Systems (March) – Belo Horizonte – Minas Gerais – Brazil.
20176 activities
International Conference on Applied Mathematics and Informatics (ICAMI) – Critical Length Phenomenon For a Class of Dispersive Systems (November/December) – San Andrés – Colombia.Third Workshop on Nonlinear Dispersive Equations – General Boundary Value Problems of the Kortweg-de Vries Equation on a Bounded Domain (November) – Campinas – São Paulo – Brazil.MATFEST 2017 – Instituto de Matemática UFAL – Teoria do Controle: das EDO’s às EDP’s (Outubro) – Maceió – Alagoas – Brazil.VI WENLU Workshop em Equações Diferenciais Não-Lineares da UFPB – Critical Length Phenomenon For a Class of Dispersive Systems (March) – João Pessoa – Paraíba – Brazil.Recife Workshop on Control & Stabilization of PDEs (February) – Recife – Brazil.ICMC Summer Meeting on Differential Equation – Controllability of the Nonlinear Schrödinger Equation in Exterior Domains (February) – São Carlos – São Paulo – Brazil.
20163 activities
ENAMA – Encontro Nacional de Análise Matemática e Aplicações – Some results of internal controllability for the Korteweg-de Vries equation in the bounded domain (November) – Niterói – Rio de Janeiro – Brazil.Nonlinear PDEs @ IMPA – Neumann boundary controllability of the Korteweg-de Vries equation (June) – Rio de Janeiro – Rio de Janeiro – Brazil.V WENLU Workshop em Equações Diferenciais Não-Lineares da UFPB – Exact Controllability of the Nonlinear Schrödinger Equation in Exterior Domains (February) – João Pessoa – Paraíba.
20152 activities
Theoretical, Numerical and Experimental Studies of Nonlinear Dispersive Water Waves – Internal controllability results of the Korteweg-de Vries equation (July) – Tsinghua Sanya International Mathematics Forum – Sanya – China.Workshop on Control System and Identification Problems – Boundary controllability of the Korteweg-de Vries equation (January) – Valparaíso – Chile.
20143 activities
The 34th Southeastern Atlantic Regional Conference on Differential Equation – Some control results for the Boussinesq system of KdV-KdV type (October) – University of Memphis. Memphis – USA.Harmonic Analysis & Partial Differential Equations: Recent Developments & Future Directions: A conference in honor of C.E. Kenig (September) – University of Chicago. Chicago – USA.ICMC Summer Meeting on Differential Equation – Some controllability results for the Korteweg-de Vries equation (February) – São Carlos, SP – Brazil.
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04Collaborators

A research networkacross borders.

Colleagues and co-authors connected through partial differential equations, control theory, and numerical analysis.

F. D. ArarunaBrazilG. J. BautistaBrazilK. BhandariCzech RepublicP. Braz e SilvaBrazil
M. A. CaicedoColombia
J. D. N. CarvalhoBrazilM. CavalcanteBrazilE. CerpaChileB. ChentoufKuwaitJ. S. da SilvaBrazilD. dos Santos FerreiraFranceI. de JesusBrazilL. de SousaBrazilG. DoroninBrazilF. A. GallegoColombiaM. GomesBrazilA. GomesBrazilV. H. Gonzalez MartinezBrazilH. ParadaFranceC. KwakSouth KoreaV. KomornikFranceJ. LímacoBrazilS. MajumdarIndiaJ. R. MuñozChileJ. C. MuñozColombiaA. C. NascimentoBrazilA. PampuBrazilA. PazotoBrazilJ. R. QuinteroColombiaL. RosierFranceO. Sierra FonsecaBrazilS.-M. SunUnited StatesT. Y. TanakaBrazilF. J. Vielma LealBrazilB.-Y. ZhangUnited States
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05Administrative duties

Academic service,quietly at work.

Current leadership and long-term service supporting mathematics at UFPE.

Coordinator

Graduate Program in Mathematics at the Federal University of Pernambuco.

Board member

Center for Exact and Natural Sciences (CCEN) at the Federal University of Pernambuco.

Permanent faculty member

Graduate Program in Mathematics at the Federal University of Pernambuco.

View previous duties3 earlier appointments

Vice coordinator

Graduate Program in Mathematics at the Federal University of Pernambuco.

Faculty member

Mathematics Degree Program at the Federal University of Pernambuco.

Vice coordinator

Graduate Program in Mathematics at the Federal University of Pernambuco.

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06Mentoring

From first questionsto independent research.

6 current3 postdocs23 former students

Current supervision

Research in progress

PhD, Master’s, and scientific initiation students currently developing projects at UFPE.

Scientific initiation

Raphael Thales Andrade

Introdução às EDOs e aplicações em teoria do controle

08/2026—Current · PICME / CNPq

Postdoctoral supervision

Advanced research stays

A compact record of postdoctoral researchers supervised at UFPE.

Postdoc

Victor Hugo Gonzalez Martinez

08/2021—09/2022 · FACEPEPostdoc

Ademir Benteus Pampu

04/2019—04/2021 · CAPESPostdoc

Andressa Gomes

05/2020—03/2021 · CAPES

Former students

Recent alumni

Recent doctoral work remains visible; the complete mentoring history opens only when requested.

Defense · 07/2025

Jandeilson Santos da Silva

Control results of Korteweg-de Vries type equations

CNPqDefense · 11/2024

Juan Ricardo Muñoz Galeano

Control and Stabilization of KdV-KdV and KP type systems

FACEPEDefense · 08/2024

Jackellyny Dassy do Nascimento Carvalho

Control and stabilization for the nonlinear Schrödinger equation

CNPqDefense · 07/2023

Isadora Maria de Jesus

Well-posedness and stabilization theory for dispersive system

—
View all 23 former studentsPhD · Master’s · Scientific initiation

PhD

2

Master’s degree

5
Jefferson Henriques Bezerra

Controle nulo da equação do calor unidimensional: Uma análise matemática e numérica

Defense · 07/2024 · FACEPE
Érick Caetano Alves do Nascimento

Propriedade de controle ótimo tipo bang-bang para equação de Korteweg-de Vries-Burgers

Defense · 07/2024 · CNPq
Hugo Deleon Pereira de Medeiros

Estabilização para um sistema acoplado tipo KdV-KdV

Defense · 07/2018 · —
Elthon Matheus Araújo

Controle e estabilização para a equação de Korteweg-de Vries em um domínio periódico

Defense · 07/2018 · CNPq

Scientific initiation

12
Pedro Gabriel Lira Lima Farias

Teoria da Medida e Aplicações

08/2025—07/2026 · FACEPE
Pedro Sales Vital

Teoria da Medida e Aplicações

04/2024—08/2024 · CNPq
Pedro Gabriel Lira Lima Farias

Equações diferenciais ordinárias e aplicações

08/2024—07/2025 · —
Raffael Marinho de Arruda Feitosa

Equações diferenciais ordinárias e aplicações

08/2022—07/2023 · FACEPE
Daniel Alves de Lima

Teoria do Controle para EDO’s

08/2021—02/2022 · FACEPE
Daniel Alves de Lima

Teoria do Controle para Equações Diferenciais Parciais

02/2021—07/2021 · —
Guilherme Araújo

Equações Diferenciais Ordinária e Aplicações à Teoria do Controle

10/2020—07/2021 · CNPq
Mateus Ferreira de Melo

Teoria do controle para equações diferenciais parciais

09/2020—01/2021 · CNPq
Mateus Ferreira de Melo

Medida, Integração e Aplicações

08/2019—09/2020 · PROPESQ / UFPE
Mateus Ferreira de Melo

Análise Funcional e Aplicações

08/2018—07/2019 · PROPESQ / UFPE
Rafael Marques Cavalcante Neto

Teoria do Controle Aplicada às EDO’s

08/2018—07/2019 · PROPESQ / UFPE
Mateus Ferreira de Melo

Teoria do Controle Aplicada às EDO’s

08/2017—07/2018 · FACEPE
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07Academic life

Teaching

Courses built around rigorous thinking.

Current and previous courses for undergraduate and graduate students at UFPE.

Undergraduate Graduate

Mentoring

Guidance from first questions to new results.

Supervision of students and postdoctoral researchers in analysis, control, and dispersive equations.

Current mentoring Former students

Community

Research grows through conversation.

Seminars, collaborations, and research groups connecting PDE scholars in Brazil and abroad.

PDE seminar Research group
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08Connect

Find my workacross the field.

Google ScholarMathSciNetORCIDarXivResearchGateScopus
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