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Análise de um sistema parabólico semi-linear com não-linearidade não-localSILVA, Isis Gabriella de Arruda Quinteiro 31 January 2010 (has links)
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Previous issue date: 2010 / Universidade Federal Rural de Pernambuco / Estudamos o sistema parabólico não-local acoplado
ut − Δu = ∫ t
0
(t − s)−1 |v|p−1v(s)ds, vt − Δv = ∫ t
0
(t − s)−2 |u|q−1u(s)ds
onde 0 ≤ γ1, γ2 < 1 e p, q ≥ 1. Consideramos o problema em (0, T)×RN e um problema de
Dirichlet em (0, T)×Ω, com Ω ⊂ RN domínio limitado e fronteira regular. Admitimos que
os dados iniciais u(0), v(0) ∈ C0(RN) e u(0), v(0) ∈ C0(Ω), respectivamente. Encontramos
condições que garantem a existência de solução global e a explosão num tempo finito de
qualquer solução do sistema em questão
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Deux aspects de la géométrie birationnelle des variétés algébriques : la formule du fibré canonique et la décomposition de Zariski / Two aspects of birational geometry of algebraic varieties : The canonical bundle formula and the Zariski decompositionFloris, Enrica 25 September 2013 (has links)
La formule du fibré canonique et la décomposition de Fujita-Zariski sont deux outils très importants en géométrie birationnelle. La formule du fibré canonique pour une fibration f:(X,B)→ Z consiste à écrire K_X+Bcomme le tiré en arrière de K_Z+B_Z+M_Z o* K_Z est le diviseur canonique, B_Z contient des informations sur les fibres singulières et M_Z est appelé partie modulaire. Il a été conjecturé qu’il existe une modification birationnelle Z' de Z telle que M_Z' est semi ample sur Z' , o* M_Z' est la partie modulaire induite par le changement de base. Un diviseur pseudo effectif D admet une décomposition de Fujita-Zariski s’il existent un diviseur nef P et un diviseur effectif N tels que D=P+N et P est "le plus grand diviseur nef" avec la propriété que D−P est effectif. / The canonical bundle formula and the Fujita-Zariski decomposition are two very important tools in birational geometry. The canonical bundle formula for a fibration f:(X, B)→Z consists in writing K_X+B as the pul lback of K_Z+B_Z+M_Z where K_Z is the canonical divisor, B_Z contains informations on the singular fibres andM_Z is called moduli part. It was conjectured that there exists a birational modification Z' of Z such that M_Z'is semi ample on Z', where M_Z' is the moduli part induced by the base change. A pseudo effective divisor Dadmits a Fujita-Zariski decomposition if there exist a nef divisor P and an effective divisor N such that D=P+N and P is "the biggest nef divisor" such that D−P is effectve.
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Problemas parabólicos com resultados tipo Fujita em domínios arbitráriosMALDONADO, Ricardo Donato Castillo 19 February 2016 (has links)
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Previous issue date: 2016-02-17 / Estudamos condições de existência e não existência de soluções globais para um sistema
acoplado de equações parabólicas não lineares e para um problema parabólico com expoente
variável. Em ambos os casos, consideramos um domínio arbitrário de RN com fronteira
regular e com condições de Dirichlet na fronteira. Como consequência destes resultados é
possível determinar o coe ciente de Fujita destes problemas. / We study conditions for existence and non existence of global solutions for a nonlinear coupled
parabolic systems and for parabolic problem with variable exponent. In both cases, we
consider an arbitrary domain of RN with smooth boundary and Dirichlet condition on the
boundary. As consequence of these results is possible to determinate the Fujita's exponent
of ones.
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