Research
Research interests
Dispersive systems
Asymptotic properties of PDEs
Control theory of PDEs
Initial-boundary value problem of PDEs
Preprints
P. Braz e Silva, R. A. Capistrano-Filho, J. D. N. Carvalho, D. dos Santos Ferreira, Control of the Schrödinger equation in R^3: The critical case, submitted. (article)
R. A. Capistrano-Filho and J. S. da Silva, Boundary controllability of the Korteweg-de Vries equation: The Neumann case, submitted. (article)
R. A. Capistrano-Filho, V. Komornik, and A. F. Pazoto, Observability of the linear Zakharov-Kuznetsov equation, submitted. (article)
R. A. Capistrano-Filho, J. R. Quintero and S.-M. Sun, Stability of solitary waves for generalized abcd-Boussinesq system: The Hamiltonian case, submitted. (article)
R. A. Capistrano-Filho, F. Gallego and V. Komornik, A qualitative study of the generalized dispersive systems with time-delay: The unbounded case, submitted. (article)
R. A. Capistrano-Filho, L. S. de Sousa and F. A. Gallego, Approximation theorem for the Kawahara operator and its application in control theory, submitted. (article)
R. A. Capistrano-Filho and T. Y. Tanaka, Controls insensitizing the norm of solution of a Schrödinger type system with mixed dispersion, submitted. (article)
Accepted papers
R. A. Capistrano-Filho, V. H. Gonzalez Martinez and J. R. Muñoz, Stabilization of the Kawahara-Kadomtsev-Petviashvili equation with time-delayed feedback, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, to appear. (article)
R. A. Capistrano-Filho, B. Chentouf, and I. M. de Jesus, On the stability of the Kawahara equation with a distributed infinite memory, Mathematical Control and Related Fields, to appear. (article)
Journal papers
2024
33. K. Bhandari, R. de A. Capistrano-Filho, S. Majumdar, and T. Y. Tanaka, Coupled linear Schrödinger equations: Control and stabilization results, Zeitschrift für Angewandte Mathematik und Physik, 75, 97 (2024). (article)
32. R. A. Capistrano-Filho, B. Chentouf, V. H. Gonzalez Martinez, and J. R. Muñoz, On the boundary stabilization of the KdV-KdV system with time-dependent delay, Nonlinear Analysis: Real World Applications, 79:104122 (2024). (article)
31. R. A. Capistrano-Filho and V. H. Gonzalez Martinez, Stabilization results for delayed fifth-order KdV-type equation in a bounded domain, Mathematical Control and Related Fields, 2024, 14(1): 284-321. (article)
30. R. A. Capistrano-Filho, B. Chentouf, and I. de Jesus, Dynamic stability of the Kawahara equation under the effect of a boundary finite memory, Qual. Theory Dyn. Syst. 23, 28 (2024). (article)
2023
29. R. A. Capistrano-Filho, I. M. de Jesus and V. H. Gonzalez Martinez, Infinite memory effects on the stability of Biharmonic Schrödinger equation, Electron. J. Qual. Theory Differ. Equ., No. 39, (2023) 1-23. (article)
28. R. A. Capistrano-Filho, L. S. de Sousa and F. A. Gallego, Control of Kawahara equation with overdetermination condition: The unbounded cases, Math. Meth. Appl. Sci. 46 (2023), 15162-15185. (article)
27. R. A. Capistrano-Filho and A. Pampu, Control results for a model of resonant interaction between short and long capillary-gravity waves, Nonlinear Differ. Equ. Appl. 30, 61 (2023). (article)
26. R. A. Capistrano-Filho and I. M. de Jesus, Massera’s theorems for a higher order dispersive system, Acta Applicandae Mathematicae, 185, 5 (2023). (article)
25. R. A. Capistrano-Filho, E. Cerpa and F. Gallego, Rapid Exponential Stabilization of a Boussinesq System of KdV–KdV Type, Communications in Contemporary Mathematics, Vol. 25, No. 03, 2150111 (2023). (article)
24. R. A. Capistrano-Filho and A. Gomes, Global control aspects for long waves in nonlinear dispersive media, ESAIM: Control, Optimisation and Calculus of Variations, 29:7 (2023), 1-47. (article)
23. R. A. Capistrano-Filho, B. Chentouf, L. de Sousa and V. H. Gonzalez Martinez, Two stability results for the Kawahara equation with a time-delayed boundary control, Zeitschrift für Angewandte Mathematik und Physik, 74, 16, (2023), 1-26. (article)
22. R. A. Capistrano-Filho, M. Cavalcante and F. A. Gallego, Controllability for Schrödinger type system with mixed dispersion on compact star graphs, Evolution Equations & Control Theory, 12(1) (2023), 1-19. (article)
2022
21. R. A. Capistrano-Filho, C. Kwak and F. J. Vielma Leal, On the control issues for higher-order nonlinear dispersive equations on the circle, Nonlinear Analysis: Real World Applications, 68:103695, (2022). (article)
20. R. A. Capistrano-Filho and A. Pampu, The fractional Schrödinger equation on compact manifolds: Global controllability results, Mathematische Zeitschrift 301, pages 3817–3848 (2022). (article)
19. R. A. Capistrano-Filho, M. Cavalcante and F. A. Gallego, Forcing operators on star graphs applied for the cubic fourth order Schrödinger equation, Discrete & Continuous Dynamical Systems - B, 27(6) (2022), 3399-3434. (article)
18. R. A. Capistrano-Filho and L. S. de Sousa, Control results with overdetermination condition for higher order dispersive system, Journal of Mathematical Analysis and Applications, 506(1) (2022), 1-22. (article)
2021
17. R. A. Capistrano-Filho and M. Cavalcante, Stabilization and control for the biharmonic Schrödinger equation, Appl Math Optim, 84 (2021) 103-144. (article)
16. R. A. Capistrano-Filho, Weak damping for the Korteweg-de Vries equation, Electron. J. Qual. Theory Differ. Equ. No. 43 (2021), 1-25. (article)
15. R. A. Capistrano-Filho and M. M. de S. Gomes, Well-posedness and controllability of Kawahara equation in weighted Sobolev spaces, Nonlinear Analysis, Volume 207 (2021), 1-24. (article)
2020
14. R. de A. Capistrano-Filho, M. Cavalcante and F. A. Gallego, Lower regularity solutions of the biharmonic Schrödinger equation in a quarter plane, Pacific Journal of Mathematics 309-1 (2020), 35-70. (article)
13. R. A. Capistrano-Filho, V. Komornik and A. F. Pazoto, Pointwise control of the linearized Gear--Grimshaw system, Evolution Equations & Control Theory, 9(3) (2020), 693-719. (article)
2019
12. R. A. Capistrano-Filho, S.-M. Sun and B.-Y. Zhang, Initial boundary value problem for Korteweg-de Vries equation: a review and open problems, São Paulo Journal of Mathematical Sciences, (2019) 13:402-417. Special Section: Nonlinear Dispersive Equations. (article)
11. R. A. Capistrano-Filho, A. F. Pazoto and L. Rosier, Control of Boussinesq system of KdV-KdV type on a bounded interval, ESAIM Control Optimization and Calculus Variations, 25 (2019), 58 1-55. (article)
10. R. A. Capistrano-Filho, F. A. Gallego and A. F. Pazoto, On the well posedness and large-time behavior of higher order Boussinesq system, Nonlinearity 32 (2019) 1852-1881. (article)
2018
9. R. A. Capistrano-Filho, S.-M. Sun and B.-Y. Zhang, General boundary value problems of the Korteweg-de Vries equation on a bounded domain, Mathematical Control and Related Fields, (2018) 8 (3-4), 583-605. Special issue dedicated to Jiongmin Yong on the occasion of his 60th birthday. (article)
8. R. A. Capistrano-Filho and F. A. Gallego, Asymptotic behavior of Boussinesq system of KdV-KdV type, J. Differential Equations 265 (2018) 2341–2374. (article)
7. R. A. Capistrano-Filho, Stabilization of the Gear--Grimshaw system with weak damping, J Dyn Control Syst (2018) 24:145. (article)
2017
6. M. A. Caicedo, R. A. Capistrano-Filho and B.-Y. Zhang, Neumann boundary controllability of the Korteweg-de Vries equation on a bounded domain, SIAM J. Control Optim., 55 (2017), no. 6, 3503–3532. (article)
5. R. A. Capistrano-Filho, F. A. Gallego and A. F. Pazoto, Boundary controllability of the nonlinear coupled system of two Korteweg-de Vries equations with critical size restrictions on the spatial domain, Math. Control Signals Syst. (2017) 29: 6. (article)
2016
4. R. A. Capistrano-Filho, F. A. Gallego and A. F. Pazoto, Neumann boundary controllability of the Gear-Grimshaw system with critical size restrictions on the spatial domain, Zeitschrift fur Angewandte Mathematik und Physik (Printed ed.), v. 67 (2016), p. 1-36. (article)
2015
3. R. A. Capistrano-Filho, A. F.Pazoto and L. Rosier, Internal controllability for the Korteweg-de Vries equation on a bounded domain, ESAIM Control Optimization and Calculus Variations 21 (2015) 1076-1107. (article)
2014
2. R. A. Capistrano-Filho, V. Komornik and A. F. Pazoto, Stabilization of the Gear-Grimshaw system on a periodic domain, Communications in Contemporary Mathematics 16 (2014) 1-22. (article)
2012
1. F. D. Araruna, R. A. Capistrano-Filho and G. Doronin, Energy decay for the modified Kawahara equation posed in a bounded domain, Journal of Mathematical Analysis and Applications 385 (2012) 743–756. (article)
Books/Chapters
R. de A. Capistrano-Filho, A note on the critical length phenomenon for the Korteweg-de Vries equation, Springer for the Series: Ghent Analysis and PDE Center, Research Perspectives, to appear.
Thesis
Contrôle d'equations dispersives pour les ondes de surfaces, Phd Thesis, Institut Élie Cartan de Lorraine, Université de Lorraine, Nancy - France (2012-2014). (tese.pdf)
Control of dispersive equations for surface waves, Tese de Doutorado, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro - Brazil (2010-2014). (tese.pdf)