EVOLUTION OF THE RADIUS OF SPATIAL ANALYTICITY FOR THE PERIODIC BBM EQUATION

Author(s)

Himonas, A. Alexandrou ^[1] ; Petronilho, Gerson ^[2]

Affiliation

^[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 - USA

^[2] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Proceedings of the American Mathematical Society; v. 148, n. 7, p. 2953-2967, JUL 2020.
• Web of Science Citations: 0

Abstract

The Cauchy problem of the Benjamin-Bona-Mahony (BBM) equation with initial data na that are analytic on the torus and have uniform radius of analyticity r(0) is considered, and the evolution of the radius of spatial analyticity r(t) of the solution u(t) at any future time t is examined. It is shown that the size of the radius of spatial analyticity persists for some time and after that it evolves in a such a way that its size at any time t is bounded below by ct(-1) for some c > 0. The optimality of this bound remains an open question. (AU)

• FAPESP's process: 12/03168-7 - Geometric theory of PDE and several complex variables
• Grantee: Jorge Guillermo Hounie
• Support Opportunities: Research Projects - Thematic Grants