Título: Singular perturbations and optimal control of stochastic systems in infinite dimension

Palestrante: Andrzej Święch (Georgia Institute of Technology)

Data: 22/04/2021
Horário: 11:00h
Local: Transmissão online.

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Palestra: Controllability properties of anomalous diffusion phenomena
Palestrante: Sorin Micu (University of Craiova and Institute of Statistical Mathematics and Applied Mathematics, Romênia)

Data: 23/01/2020
Horário: 11h
Sala: C116

Resumo: Many physical phenomena are characterized by an anomalous diffusion when the mean square displacement of a particle will grow at a nonlinear rate in time. Some typical examples are the subdiffusional mobility of the proteic macromolecules in overcrowded cellular cytoplasm and the smoke's superdiffusion in turbulent atmosphere. We consider a simple one dimensional linear model which describes an anomalous diffusive behavior, involving a fractional Laplace operator, and we study its controllability property. If the fractional power of the Laplace operator is less or equal than 1/2 we are dealing with a subdiffusion phenomenon and the system is not spectrally controllable. The aim of the paper is twofold. Firstly, to analyze the possibility of controlling a finite number N of eigenmodes of the solution and to find the behavior of the corresponding controls when N tends to infinity. Secondly, to investigate the null-controllability property of the system when the support of the control moves linearly with respect to time.

Palestra: The cubic fourth order Schrödinger equation on a star graph
Palestrante: Fernando Gallego (Universidad Nacional de Colombia (campus de Manizales))

Data: 13/02/2020
Horário: 11h
Local: Sala - C116

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Titulo: Nonradial blow-up solutions for the Zakharov system
Palestrante: Juan C. Cordero Ceballos (UNAL, Colômbia)

Data: 02/10/2019
Horário: 12:00
Local: Sala - C116

Resumo: We will show that there are nonradial solutions for the Zakharov equations, which have blow-up in finite time in the case of negative energy, due to a virial identity of momentum type. This solutions are standing waves for the Zakharov-Rubenchik system, so we give response to two questions proposed by F. Merle in [1].

References:
[1] F. Merle, Blow-up results of virial type for Zakharov Equations, Communications in Mathematical Physics, 175, 433-455 (1996)
[2] J. C. Cordero, Supersonic limit for the Zakharov-Rubenchik system, Journal Differential Equations, 261 (2016), 5260-5288
[3] J. R. Quintero, J.C. Cordero, Instability of the standing waves for a Benney-Roskes/Zakharov-Rubenchik system and blow-up for the Zakharov equations, Discrete and Continuous Dynamical Systems Series B doi:10.3934/dcdsb.2019217