Palestras e Seminários
15/03/2023
14:00
Auditório Luiz Antonio Fávaro - Sala 4111
Palestrante: Maykel Boldrin Belluzi
https://sites.google.com/view/sdnl-icmc-usp/seminarios
Responsável: Estefani Moraes Moreira (estefani@usp.br)
Resumo: In this talk we study fractional powers of linear operators and its connections with PDEs, focusing on using this theory to approximate hyperbolic problems by parabolic ones. To illustrate this idea, we consider cascade systems of PDEs, where the fractional approximations are explicitly calculated and we discuss local solvability of the fractional equation with subcritical nonlinearity. As an example, a cascade system of Schrödinger equation is analyzed and a connection between the fractional system and the original system is established.
References:
[1] Belluzi, M. B., Bezerra, F., and Nascimento, M. J. D. On spectral and fractional powers of damped wave equations. Commun. Pure Appl. Anal. 21, 8 (2022).
[2] Belluzi, M., Nascimento, M. J. D., and Schiabel, K. On a cascade system of Schrödinger equations. Fractional powers approach. J. Math. Anal. Appl. 506, 1 (2022).
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