Assymptotic behaviour of solutions to the Cauchy problem for systems of evolution partial differential equations

• Grant number: 22/01712-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2022
• End date: August 04, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo Rempel Ebert
• Grantee: Alexandre Arias Junior
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

In this project, we are interested in the asymptotic behavior (in time) of solutions to the Cauchy problem for semi-linear systems of evolution partial differential equations in Lebesgue Lp, Sobolev or Besov spaces. More precisely, we plan to apply the well known estimates for solutions to the associate linear problems to obtain necessay and sufficient conditions for the existence of global solutions in time for semi-linear problems, possibly assuming small initial data. Also blow-up results and the life-span of solutions are topics of interest. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ARIAS JUNIOR, ALEXANDRE ARIAS; ASCANELLI, ALESSIA; CAPPIELLO, MARCO. KdV-type equations in projective Gevrey spaces. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 178, p. 31-pg., 2023-10-01. (22/01712-3)