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Seminario de Ecuacións Diferenciais e Análise Funcional

Fractional powers of linear operators associated to cascade systems of PDEs

07.03.2023 | 13.00h-14.00h

Seminario de Análise Matemática

Maykel Boldrin Belluzi. Instituto de Ciências Matemáticas e de Computação – ICMC (Universidade de São Paulo – USP)

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).

Los contenidos de esta página se actualizaron el 06.03.2023.