Fractional powers of linear operators associated to cascade systems of PDEs

"Fractional powers of linear operators associated to cascade systems of PDEs", organizado polo CITMAga. Será impartido por Maykel Boldrin Belluzi (Universidade de São Paulo–USP)

Data: martes 7 de marzo

Hora: 13:00 h.

Duración: 1 hora

Lugar: Seminario de Análise Matemática (Facultade de Matemáticas, USC)

Abstract:

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).