Felipe Poblete Homepage

Welcome

In this space you will find my work products and other research-related aspects

Associate Professor of Institute of Physical and Mathematical Sciences, University Austral of Chile, Valdivia, Chile.

PhD in Sciences mention Mathematics in 2013 at the University of Chile.

My research interests are in Dispersive Partial Differential Equations, theory of semigroups and resolvent families of Evolution Equations.

Publications

J. Faya, P. Figueroa, C. Muñoz, and F. Poblete, "Uniqueness of quasimonochromatic breathers for the generalized Korteweg-de Vries and Zakharov-Kuznetsov models," arXiv preprint arXiv:2404.09100, 2024.
F. Alegría, G. Chen, Gong, C. Muñoz, F. Poblete, B. Tardy, "On uniqueness of KP soliton structures", to appear in Journal of Differential Equations.
V. Castillo, C. Muñoz, F. Poblete, and V. Salinas, "The Generalized Riemann Zeta heat flow," Journal of Functional Analysis, 110879, 2025.
A. J. Mendez, C. Muñoz, F. Poblete, and J. C. Pozo, "Long time asymptotics of large data in the Kadomtsev–Petviashvili models," Nonlinearity, vol. 37, no. 5, p. 055017, 2024.
M. Pinto, F. Poblete, and Y. Xia, "New class of perturbations for nonuniform exponential dichotomy roughness," Journal of Differential Equations, vol. 393, pp. 369-412, 2024.
F. Poblete, C. Silva, and A. Viana, On the Boussinesq system with fractional memory in pseudo-measure spaces, Asymptotic Anal. 139, No. 3-4, 157-181, 2024.
F. Poblete, V. Poblete, and J. C. Pozo. Wellposedness of second order evolution equations. Complex Analysis and Operator Theory, 17(3):1–26, 2023.
M. Pinto, F. Poblete, and D. Sepúlveda. Approximation of mild solutions of delay differential equations on banach spaces. Journal of Differential Equations, 303:156–182, 2021.
A. J. Mendez, C. Muñoz, F. Poblete, and J. C. Pozo. On local energy decay for large solutions of the zakharov-kuznetsov equation. Communications in Partial Differential Equations, 46(8):1440–1487, 2021.
C. Kwak, C. Munoz, F. Poblete, and J. C. Pozo. The scattering problem for hamiltonian abcd boussinesq systems in the energy space. Journal de Mathématiques Pures et Appliquées, 27:121–159, 2019.
V. Poblete, F. Poblete, and J. C. Pozo. Strong solutions of a neutral type equation with finite delay. Journal of Evolution Equations, 19(2):361–386, 2019.
M. Pinto, F. Poblete, and D. Sepúlveda. Abstract weighted pseudo almost automorphic functions, convolution invariance and neutral integral equations with applications. J. Integral Equations Applications 31 (4), 571-622, 2019.
C. Muñoz, F. Poblete, and J. C. Pozo. Scattering in the energy space for boussinesq equations. Communications in Mathematical Physics, 361:127–141, 2018.
C. Lizama and F. Poblete. A characterization of well-posedness for abstract cauchy problems with finite delay. Journal of mathematical analysis and applications, 457(1):410–435, 2018.
C. Lizama, P. J. Miana, and F. Poblete. Uniform stability of (a, k)-regularized families. Asymptotic Analysis, 84(1-2):47–60, 2013.
C. Lizama and F. Poblete. Regularity of mild solutions for a class of fractional order differential equations. Applied Mathematics and Computation, 224:803–816, 2013.
C. Lizama and F. Poblete. On a functional equation associated with (a,k)-regularized resolvent families. In Abstract and Applied Analysis, volume 2012. Hindawi, 2012

Projects

2024-2025 Math-AmSud 23-MATH-18 WAFFLE "Waters, Atmosphere, Fluids and Friedman-Lemaître evolutions". International Project Coordinator. (https://sites.google.com/view/mathamsud-waffle/home)
2024-2026. Chilean member of the PANDA joint effort (https://team.inria.fr/panda/), dealing with Boussinesq and Nonlinear Schrödinger models in a domain under physically variable bottom, both from the theoretical and numerical point of view.
2022-2026 ANID Fondecyt 1221076 "Towards a complete rigorous description of the long-time dynamics in the Kadomtsev-Petviashvili models of fluids" Regular Fondecyt project on the long time description of solutions for Kadomtsev-Petviashvili models. Responsible Researcher.
2022-2025 ANID Exploration Project "The PDE approach in two number theoretical monster problems" Exploration project on mathematics of the Collatz and Heat complex models. Alternate Director.
2018 - 2021, ANID Fondecyt Initiation 11181263. ''Mild Well Posedness of Abstract Evolution Equations and Scattering in the Energy Space''. Fondecyt project on the long time description of solutions for abstract evolution equations and properties of scattering in some dispersive models. Responsible Researcher.
2017 - 2021, Fondecyt Regular 1170466. "Dichotomy, Stable Manifolds, Linearization and Numerical Approximation in Differential Equations with Variable Deviations". Co-Researcher. Project on the study of different properties in Differential Equations with variable deviations.
2017 - 2019, DID-UACh S-2017-43. "Qualitative Properties for First Order Equations with Delay and Neutral Integral Equations on Banach Spaces." Responsible Researcher.

Outreach activities

Alphanumeria

This initiative consists of a music band formed by a multidisciplinary group from UACh. I am one of his members. Alphanumeria aims to reveal how Mathematics is immersed in different sciences and societies (see www.alphanumeria.cl).

Some of our activities:

Alphanumeria’s presentation in “Annual Meeting of the Mathematical Society of Chile " Valdivia, 2024.
Alphanumeria’s Concert in “The shape of water” Science’s Festival, Territory, and Art. Valdivia, 2023.
Alphanumeria musical presentation, Science Festival, Radio University Austral of Chile, 2022 (Youtube link).
Music stand Alphanumeria, Centro de Ski y Montañismo Antillanca, Osorno, 2020.
Music stand Alphanumeria, Costanera Science Festival, Valdivia , 2019.
Musical presentation Alphanumeria Gymnasium School in Río Bueno, 2018

Scientific advisor for school research

Puenteulerizando (2022): Research proposed using graph theory how to build new bridges in Valdivia, solving the city's connectivity problem. Selected team to represent Los Ríos region.
Cubometría (2019): research proposed an study of tilings in general figures composed by cubes.
Tilings of a cube (2018): research that proposed a way to describe all regular tilings of a cube.

Administrative Work

Director of the newly established Master's program in Mathematics at the UACh. I was also a member of the committee responsible for the creation of this program.
Member of the Cientific Committee of XCII Annual Meeting of the Mathematical Society of Chile, UACh, Valdivia, 2024.
Member of the Organizing Committee of 1st and 2nd Symposium on Partial Differential Equations and Number Theory, UACh, Valdivia 2023 and 2024.
Member of the Organizing Committee of the sesion Differential Equations in the XXXV Conference on Mathematics in the Southern Zone, Concepción, 2023.
Since 2018, Representative of the Universidad Austral de Chile in the permanent committee of the Conference on Mathematics in the Southern Zone.
Member of the Organizing Committee of Second Workshop on Evolution Equations in Valdivia 2016, (https://eventos.cmm.uchile.cl/valdivia2016/)
Director of the Organizing Committee for the Conference on Mathematics in the Southern Zone 2018, (https://www.jmzs.cl/2018/)
Member of the committee for the new strategic plan of the Faculty of Sciences 2021-2025, University Austral of Chile.

Students

Rodrigo Fernandez (undergraduate) UACh. Adviser: Felipe Poblete, 2024. Thesis title: Nuevas propiedades de soluciones en los modelos KP. Partially funded by ANID Fondecyt Regular 1221076.
Vicente Salinas (ANID PhD Fellowship and ANID Exploration 2022 project), U. Chile. Advisers: Claudio Muñoz and Felipe Poblete. Expected defense: December 2026. Thesis title: The generalized Riemann Heat flow.
Benjamín Tardy (CMM Master Fellowship) U. Chile. Advisers: Felipe Poblete and Claudio Muñoz, 2024. Thesis title: Uniqueness in KP-II multi-solitons. Partially funded by ANID Fondecyt Regular 1231250 and 1221076.
Juan Molina (undergraduate) UACh. Adviser: Felipe Poblete, 2024. Partially funded by ANID Fondecyt Regular 1221076.
Jaime Pincheira (undergraduate) UACh. Adviser: Felipe Poblete. Tesis Title: “Decay of solutions in the self-similar region of the Korteweg-De-Vries equation”. Partially funded by ANID Fondecyt Iniciación 11181263.
Luis Sobarzo (undergraduate) UACh. Adviser: Felipe Poblete. Tesis Title: “DEPCA Approximation of mild solution of the one-dimensional heat equation with delay”. Partially funded by ANID Fondecyt Iniciación 11181263.
Sebastián Antri (undergraduate) UACh. Adviser: Felipe Poblete. Tesis Title: “Resolent families with delay”. Partially funded by ANID Fondecyt Iniciación 11181263.

Talks

On uniqueness of KP soliton structures. First WAFFLE Meeting in Ecuador. March 10 to 13, Ecuador. 2025.
Nonexistence and uniqueness of breathers for modified Zakharov-Kuznetsov models. CMM PDE Seminar, Santiago, Chile. 2025.
The scattering problem for Hamiltonian ABCD Boussinesq systems in the energy space, First Workshop PANDA Lille-Santiago September 5-6, Chile. 2024.
Uniqueness of quasimonochromatic breathers for the generalized Korteweg-de Vries and Zakharov-Kuznetsov models, VII Latin American and Caribbean Congress of Mathematics, João Pessoa, Brazil. 2024.
Nonexistence and uniqueness of breathers for the Zakharov-Kuznetsov models, XCI Annual Meeting of the Mathematical Society of Chile, Santiago, Chile. 2023.
Alphanumeria, XCI Annual Meeting of the Mathematical Society of Chile, Santiago, Chile. 2023.
Kadomtsev-Petviashvili models: Temporal dynamics and special solutions, Mathematics Colloquium, University of Talca, Talca, Chile. 2023.
Long-time asymptotics of large data in the Kadomtsev-Petviashvili models and geometrical aspects of its dynamics, CMM PDE Seminar, Santiago, Chile. 2023.
Holomorphic Flow of the Riemann Zeta Function, 1st National Symposium on Partial Differential Equations and Number Theory, Valdivia, Chile. 2023.
Dynamics of Solutions of the Collatz Flow, 1st National Symposium on Partial Differential Equations and Number Theory, Valdivia, Chile. 2023.
Long-time asymptotics of large data in the Kadomtsev-Petviashvili models, XC Annual Meeting of the Mathematical Society of Chile, Punta de Tralca, Chile. 2022.
Long-time asymptotics of large data in the Kadomtsev-Petviashvili models, New Trends in Mathematics of Dispersive, Integrable, and Nonintegrable Models in Fluids, Waves, and Quantum Physics, Banff, Canada. 2022.
On local energy decay for large solutions of the Zakharov-Kuznetsov equation, XXXIV Southern Mathematical Conference, Osorno, Chile. 2022.
Long-time asymptotics of large data in the Kadomtsev-Petviashvili models, XXXIII Southern Mathematical Conference, Temuco, Chile. 2021.
Fundamental Solution of Delayed Evolution Equations in Banach Spaces, Las Palmeras Colloquium, University of Chile, Santiago, Chile. 2020.
Weak Well-Posedness for Second Order Equations with Damping, Tribute to Women in Mathematics Dedicated to Maria Isabel del Rio and Sonia Berger, University Austral of Chile, Valdivia, Chile. 2019.
A Characterization of Well-Posedness for Abstract Cauchy Problems with Finite Delay, XXXII Southern Mathematical Conference, University of Magallanes, Punta Arenas, Chile. 2019.
A Characterization of Well-Posedness for Abstract Cauchy Problems with Finite Delay, CAPDE Seminar, University of Chile (CMM), Santiago, Chile. 2018.
A Characterization of Well-Posedness for Abstract Cauchy Problems with Finite Delay, VII International Symposium of Applied Mathematics, Universidad Mayor de San Marcos, Lima, Peru. 2017.
L^p-Maximal Regularity of Second Order Evolution Equations on the Line, CAPDE Seminar, University of Chile (CMM), Santiago, Chile. 2017.
Convolution Invariance of Weighted Almost Automorphic Functions and Abstract Neutral Integral Equations, 3rd Workshop on Evolution Equations and Applications, Universidad de la Frontera, Temuco, Chile. 2017.
Functional Equations Associated with Evolution Equations, Mathematics Colloquium, Universidad Austral de Chile, Valdivia, Chile. 2016.
On a Functional Equation Associated with a First Order Problem with Finite Delay, IX GAVEFOL Congress, São Paulo, Brazil. 2014.
A Functional Equation for (a, k)-Regularized Families, Rubio de Francia Seminar organized by the Department of Mathematics, University of Zaragoza, Zaragoza, Spain. 2012.
Uniform Stability of (a, k)-Regularized Families, VII Congress of Functional Analysis and Evolution Equations (GAFEVOL), USACh, Santiago, Chile. 2012.
Maximal Regularity of First Order Differential Equations with Finite Delay on L^p, COMCA 2012, University of Antofagasta, Antofagasta, Chile. 2012.
Uniform Stability for (a, k)-Regularized Families, XXIV Southern Mathematical Conference, Universidad de la Frontera, Temuco, Chile. 2011.
A Functional Equation for (a,k)-Regularized Families, Fifth GAFEVOL Workshop, USACh, Santiago, Chile. 2010.

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