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Master's Dissertation
DOI
10.11606/D.55.2006.tde-26022007-163308
Document
Author
Full name
Gabriel Gonçalves União
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2006
Supervisor
Committee
Morales, Eduardo Alex Hernandez (President)
Gentile, Claudia Buttarello
Ladeira, Luiz Augusto da Costa
Title in Portuguese
Teoria de semigrupos e aplicações a equações impulsivas com retardamento dependendo do estado
Keywords in Portuguese
Equações funcionais com retardo dependendo do estado
Equações impulsivas
O Problema de Cauchy abstrato
Teoria de semigrupos
Abstract in Portuguese
Neste trabalho estudaremos a existência de soluções fracas para uma classe de equações diferenciais funcionais impulsivas com retardamento dependendo do estado modeladas na forma 'x POT. PRIME'(t) = Ax(t) + f(t;' x IND. p(t, xt)), t 'PERTENCE A'I = [0,a], 'x IND. 0' =\varphi 'PERTENCE A' B, 'DELTA' 'x(t IND. i) = 'I IND.i'i('x IND.i'); i = 1, ...n, onde A é o gerador infinitesimal de um 'C IND. 0'-semigrupo compacto de operadores lineares limitados ('T'(t))t '. OU ='0 definido em um espaço de Banach X; as fun»ções 'x IND. s' : (- 'INFIINITO', 0] 'SETA' X, 'x IND. s' ( teta') = x(s + 'teta'), estão em um espaço de fase B descrito axiomaticamente; f : I X B 'seta' X, 'rô' : I X B 'SETA' ( - 'INFINITO', a], 'I IND. i' : B 'SETA'X, i=1, ...n , são funções apropriadas; 0 < 't IND.1' <... < 't IND. n' < a são n¶umeros pré-fixados e o símbolo 'DELTA''ksi'(t) = 'Ksi'('t POT. + ) - 'ksi'( 't POT. -).
Title in English
Semigroup theory and applications to impulsive differential equation with state-dependent delay
Keywords in English
Functional differential equations with state-dependent delay
Impulsive differential equations
Semigroup theory
The Abstract Cauchy problem
Abstract in English
In this work we stablish the existence of mild solutions for an impulsive abstract functional differential equation with state-dependent delay described in the form 'x POT. PRIME'(t) = Ax(t) + f(t;' x IND. p(t, xt)), t 'BELONGS'I = [0,a], 'x IND. 0' =\varphi 'IS CONTAINED' B, 'DELTA' 'x(t IND. i) = 'I IND.i'i('x IND.i'); i = 1, ...n, where A is the infinitesimal generator of a compact 'C IND. 0'-semigroup of bounded linear operators ('T'(t))t '. OU ='0 defined on a Banach space X; the functions 'x IND. s': ( - INFINito, 0] 'SETA X, 'x IND. s'('teta') , belongs to some space B described axiomatically; f : I X B 'seta' X, 'rô' : I X B 'SETA' ( - 'INFINITO', a], 'I IND. i' : B 'SETA'X, i=1, ...n , são funções apropriadas; 0 < 't IND.1' <... < 't IND. n' < a são n¶umeros pré-fixados e o símbolo 'DELTA''ksi'(t) = 'Ksi'('t POT. + ) - 'ksi'( 't POT. -).
 
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dissertacao_gabriel.pdf (507.27 Kbytes)
Publishing Date
2007-02-28
 
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