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Tópicos de interesse
Tenho me dedicado ao estudo propriedades globais de operadores (pseudo)diferenciais lineares evolução t-periódicos. definidos em variedades compactas. Alguns tópicos de investigação são:
Hipoeliticidade/resolubilidade globais em variedades compactas compactas, não compactas, com bordo ou sem.
Espaços de Gevrey e Gelfand-Shilov
Variedades assintóticamente Euclidianas.
Publicações
2026
de Ávila Silva, F., Cappiello, M., Kirilov, A. Global hypoellipticity for systems in time-periodic Gelfand-Shilov spaces. (Journal of Functional Analysis).
2025
de Ávila Silva, F., Coriasco, S., Bonino, M.; Global hypoellipticity and solvability for a class of evolution operators in time-periodic weighted Sobolev spaces (Math. Annalen) (Arxiv)
de Ávila Silva, F., Medeira, C. Globally solvable complexes of pseudo-differential operators on the torus (Math. Zeitschrift)
de Ávila Silva, F., Coriasco, S., Bonino, M. Global hypoellipticity for a class of time-periodic operators on asymptotically Euclidean manifolds. (Arxiv)
de Ávila Silva, F., Kirilov, A. Global Hypoellipticity for Time-Periodic Evolution Equations: Insights from Eigenfunction Expansions. (Trends in Mathematics)
2024
de Ávila Silva, F., Cappiello, M. Globally solvable time-periodic evolution equations in Gelfand-Shilov classes. (Mathematische Annalen)
de Ávila Silva, F., Cappiello, M., Kirilov, A. Systems of differential operators in time-periodic Gelfand-Shilov spaces (Annali di Matematica Pura ed Applicata)
2023
de Ávila Silva, F. Globally hypoelliptic triangularizable systems of periodic pseudo-differential operators (2023) (Math. Nachrichten).
2022
de Ávila Silva, F.; Cappiello, M. Time-periodic Gelfand-Shilov spaces and global hypoellipticity on $\T\times \R^n$ (2022) (Journal of Functional Analysis)
de Ávila Silva, F.; Machado, E. C. Global ultradifferentiable hypoellipticity on compact manifolds (2022) (AdM)
2021
de Ávila Silva, F.; Medeira, C. Global hypoellipticity for a class of overdetermined systems of pseudo-differential operators on the torus, (2021). (Ann. Mat. Pura Appl.)
2019
de Ávila Silva, F. Global hypoellipticity for a class of periodic Cauchy operators. (2019). (J. Math. Anal. Appl.)
de Ávila Silva, F.; Kirilov, A. Perturbations of globally hypoelliptic operators on closed manifolds. (2019) (Journal of Spectral Theory)
de Ávila Silva, F. ; Gonzales, R.; Kirilov, A.; Medeira, C. Global hypoellipticity for a class of pseudo-differential operators on the torus. (2019). (J. Fourier Anal. Appl.)
2018
de Ávila Silva, F. ; Gramchev, T. ; Kirilov, A. Global Hypoellipticity for First-Order Operators on Closed Smooth Manifolds. (2018). (Journal d'Analyse Mathématique).
Preprint
de Ávila Silva, F.; de Morares, W.A.A. Global properties for a class of periodic-evolution operators on compact manifolds.
de Ávila Silva, F., Cappiello, M., Kirilov, A., Tokoro, P.M., Global properties for a class of complexes of differential operators in time-periodic Gelfand-Shilov classes.
Apresentações de Trabalho
ICMC Summer Meeting on Differential Equations 2025 Chapter. Globally solvable complexes of pseudo-differential operators on the torus. 2025.
II Simpósio de Equações Diferenciais Parciais Lineares e Análise de Fourier Global properties for certain classes of linear equations on T^m x R^n. 2025.
Fourier Analysis and Partial Differential Equations II, 2024, A class of globally hypoelliptic systems of periodic pseudodifferential operators.
14th International ISAAC Congress, 2023. Global hypoellipticity for a class of systems of periodic P.D.O's.
ICMC Summer Meeting on Differential Equations, 2023. Global ultradifferentiable properties for certain linear operators on compact manifolds.
33 Colóquio Brasileiro de Matemática. IMPA, 2021; Time-periodic Gelfand-Shilov spaces and global hypoellipticity for a class of evolution equations.
International Workshop on Operator Theory and its Applications. Chapman University (US), 2021; Globally hypoelliptic time-periodic evolution equations.
Microlocal and Global Analysis, Interactions with Geometry, University of Potsdam, Alemanha, 2021; Globally hypoelliptic systems of pseudo-differential operators on the torus.
Web Seminar on Linear PDE's and Related Topics (UFPR/USP), 2020; Global hypoellipticity for a class of systems of pseudo-differential operators on the torus.
Seminari di Analisi Matematica, Torino, Itália, 2020; Globally hypoelliptic triangularizable systems of periodic pseudo-differential operators
10th Workshop on Geometric Analysis of PDEs and Several Complex Variables, Serra Negra, Brasil, 2019; Perturbations of globally hypoelliptic operators on closed manifolds.
Microlocal and Global Analysis, Interactions with Geometry, Inst. University of Potsdam, Alemanha, 2019; A class of globally hypoelliptic Cauchy operators on the torus and generalized Siegel conditions.
ICMC Summer Meeting on Differential Equations, USP, 2019; A class of globally hypoelliptic Cauchy operators on the torus and generalized Siegel conditions.
III Congresso Brasileiro de Jovens Pesquisadores em Matemática Pura, Aplicada e Estatística, UFPR, 2018; A class of globally hypoelliptic operators on manifolds.
Conference BRICS on Mathematics, Foz do Iguaçu, 2018; Global Hypoellipticity on Manifolds and Fourier Expansion of Elliptic Operators.
International Workshop on Partial Differential Equations and Complex Analysis, UFScar, 2018; Globally hypoelliptic operators on closed manifolds and perturbations.
9th Workshop on Geometric Analysis of PDEs and Several Complex Variables, Serra Negra, Brasil, 2017; Perturbations of globally hypoelliptic operators on closed manifolds.
A Life in Mathematics Generalized functions, Microlocal analysis, PDEs and Dynamical systems Conference in memory of Todor V. Gramchev. Torino, Itália, 2017; Perturbations od Globally Hypoelliptic Invariant Operators on Smooth Manifolds.
Colaborações atuais
Alessia Asacanelli - Unife (Itália)
Alexandre Kirilov - UFPR
André Kowacs - ICMC
Cleber de Medeira - UFPR
Marco Cappiello - Unito (Itália)
Matteo Bonino - Unito (Itália)
Pedro Meyer Tokoro - UFPR
Sandro Coriasco - Unito (Itália)
Wagner A. A. de Moraes - UFPR
Projetos
2024 - Atual
Propriedades globais de sistemas de operadores diferenciais em espaços de Gelfand-Shilov
Descrição: Este projeto estuda propriedades globais de sistemas de operadores diferenciais definidos em espaços de Gelfand-Shilov. Nossas investigações fornecem condições necessárias e suficientes para a resolubilidade e hipoelipticidade globais, baseada na análise dos símbolos dos operadores.
Integrantes: Fernando de Ávila Silva - Coordenador / Alexandre Kirilov - Integrante / Marco Cappiello - Integrante.
2024 - Atual
Evolution equations in time-periodic weighted Sobolev spaces
We investigate global properties of time-periodic equations in weighted Sobolev spaces.
Integrantes: Fernando de Ávila Silva - Coordenador / Sandro Coriasco - Integrante / Matteo Bonino - Integrante.
2023 - Atual
Propriedades globais de operadores de evolução em espaços de Gevrey e Gelfand-Shilov
Este projeto considera o estudo dos problemas de resolubilidade, regularidade e boa-colocação para equações de evolução lineares ou semilineares. O foco é a análise global de tais propriedades nas classes (pseudo)diferenciais agindo nos espaços de Gevrey e Gelfand-Shilov. As principais técnicas a serem utilizadas englobam estimativas de energia, propriedades assimptóticas dos operadores envolvidos e, em caso de variável temporal periódica, processos de discretização das equações em termos de séries de Fourier e dos consequentes fenômenos diofantinos..
Integrantes: Fernando de Ávila Silva - Coordenador / Marco Cappiello - Integrante.
Financiador: Conselho Nacional de Desenvolvimento Científico e Tecnológico - Bolsa.
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