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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.)

A GRADIENT FLOW GENERATED BY A NONLOCAL MODEL OF A NEURAL FIELD IN AN UNBOUNDED DOMAIN

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Author(s):
da Silva, Severino Horacio [1] ; Pereira, Antonio Luiz [2]
Total Authors: 2
Affiliation:
[1] Univ Fed Campina Grande, UAMat, Ave Aprigio Veloso 882, Caixa Postal 10-044, BR-58109970 Campina Grande, PB - Brazil
[2] Univ Sao Paulo, IME, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 51, n. 2, p. 583-598, JUN 2018.
Web of Science Citations: 1
Abstract

In this paper we consider the nonlocal evolution equation Graphic We show that this equation defines a continuous flow in both the space C-b(R-N) of bounded continuous functions and the space C-rho(R-N) of continuous functions u such that u /s=b/ rho is bounded, where rho is a convenient ``weight function{''}. We show the existence of an absorbing ball for the flow in C-b(R-N) and the existence of a global compact attractor for the flow in C-rho(R-N), under additional conditions on the nonlinearity. We then exhibit a continuous Lyapunov function which is well defined in the whole phase space and continuous in the C-rho(R-N) topology, allowing the characterization of the attractor as the unstable set of the equilibrium point set. We also illustrate our result with a concrete example. (AU)

FAPESP's process: 16/02150-8 - Perturbation of domains and asymptotic behavior for boundary value problems
Grantee:Antonio Luiz Pereira
Support type: Regular Research Grants