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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On Exponential Decay and the Markus-Yamabe Conjecture in Infinite Dimensions with Applications to the Cima System

Full text
Author(s):
Rodrigues, Hildebrando M. [1] ; Teixeira, Marco A. [2] ; Gameiro, Marcio [1]
Total Authors: 3
Affiliation:
[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Estadual Campinas, IMECC UNICAMP, Inst Matemat Estat & Ciencia Comp, Caixa Postal 6065, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Journal of Dynamics and Differential Equations; v. 30, n. 3, p. 1199-1219, SEP 2018.
Web of Science Citations: 0
Abstract

In this work we extend to infinite dimensions a previous result of Lyascenko given in finite dimensions for a class of Lipschitz functions. In particular, this extension substitutes the class of Lipschitz functions by a class of Holder functions. Then we consider applications of these results to analyze its relation with the Markus-Yamabe Conjecture in infinite dimensions. We discuss in detail a celebrated example of Cima et al. ( Adv Math 131(2): 453-457, 1997) of a nonlinear system in dimension three whose Jacobian has a unique eigenvalue of multiplicity 3, and yet an explicit unbounded solution as exists. We also present explicit solutions of the same equation that tends to 0 as . Then we look at this conjecture by considering not the properties of the whole system, but instead the properties of some solutions. Finally we present an application in an infinite dimensional Hilbert space, where we use different techniques to study the local and global asymptotic stabilities. (AU)

FAPESP's process: 13/07460-7 - Rigorous computations for PDEs
Grantee:Marcio Fuzeto Gameiro
Support Opportunities: Regular Research Grants
FAPESP's process: 16/21032-6 - Analysis of fluid dynamics data via persistent homology
Grantee:Marcio Fuzeto Gameiro
Support Opportunities: Scholarships abroad - Research
FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
Grantee:Marco Antônio Teixeira
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 16/08704-5 - Rigorous computations in dynamics
Grantee:Marcio Fuzeto Gameiro
Support Opportunities: Regular Research Grants
FAPESP's process: 15/19165-5 - Mathematical Analysis, Diferentiation, Lebesgue Integral and Functional Analysis
Grantee:Henrique Pimenta Marçal
Support Opportunities: Scholarships in Brazil - Scientific Initiation