885 resultados para Non-autonomous semilinear parabolic problems


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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of asymptotic dynamics can be reduced to finite dimensions via the invariant manifolds technique. Some practical models are considered to show wide applicability of the theory. © 2013 Society for Industrial and Applied Mathematics.

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In this paper, we prove a stability result about the asymptotic dynamics of a perturbed nonautonomous evolution equation in ℝn governed by a maximal monotone operator. Copyright © 2013 John Wiley & Sons, Ltd. Copyright © 2013 John Wiley & Sons, Ltd.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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We study the effects of management of the PT-symmetric part of the potential within the setting of Schrodinger dimer and trimer oligomer systems. This is done by rapidly modulating in time the gain/loss profile. This gives rise to a number of interesting properties of the system, which are explored at the level of an averaged equation approach. Remarkably, this rapid modulation provides for a controllable expansion of the region of exact PT-symmetry, depending on the strength and frequency of the imposed modulation. The resulting averaged models are analysed theoretically and their exact stationary solutions are translated into time-periodic solutions through the averaging reduction. These are, in turn, compared with the exact periodic solutions of the full non-autonomous PT-symmetry managed problem and very good agreement is found between the two.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction-diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter epsilon goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. (C) 2012 Elsevier Inc. All rights reserved.

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This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.

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Ubiquitination is an essential process involved in basic biological processes such as the cell cycle and cell death. Ubiquitination is initiated by ubiquitin-activating enzymes (E1), which activate and transfer ubiquitin to ubiquitin-conjugating enzymes (E2). Subsequently, ubiquitin is transferred to target proteins via ubiquitin ligases (E3). Defects in ubiquitin conjugation have been implicated in several forms of malignancy, the pathogenesis of several genetic diseases, immune surveillance/viral pathogenesis, and the pathology of muscle wasting. However, the consequences of partial or complete loss of ubiquitin conjugation in multi-cellular organisms are not well understood. Here, we report the characterization of nba1, the sole E1 in Drosophila. We have determined that weak and strong nba1 alleluias behave genetically different and sometimes in opposing phenotypes. For example, weak uba1 alleluias protect cells from cell death whereas cells containing strong loss-of-function alleluias are highly apoptotic. These opposing phenotypes are due to differing sensitivities of cell death pathway components to ubiquitination level alterations. In addition, strong uba1 alleluias induce cell cycle arrest due to defects in the protein degradation of Cyclins. Surprisingly, clones of strong uba1 mutant alleluias stimulate neighboring wild-type tissue to undergo cell division in a non-autonomous manner resulting in severe overgrowth phenotypes in the mosaic fly. I have determined that the observed overgrowth phenotypes were due to a failure to downregulate the Notch signaling pathway in nba1 mutant cells. Aberrant Notch signaling results in the secretion of a local cytokine and activation of JAK/STAT pathway in neighboring cells. In addition, we elucidated a model describing the regulation of the caspase Dronc in surviving cells. Binding of Dronc by its inhibitor Diap1 is necessary but not sufficient to inhibit Dronc function. Ubiquitin conjugation and Uba1 function is necessary for the negative regulation of Dronc. ^

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Adherens junctions (AJs) and basolateral modules are important for the establishment and maintenance of apico-basal polarity. Loss of AJs and basolateral module members lead to tumor formation, as well as poor prognosis for metastasis. Recently, in mammalian studies it has been shown that loss of either AJ or basolateral module members deregulate Yorkie activity, the downstream transcriptional effector of the Hippo pathway. Importantly, it is unclear if AJ and basolateral components act through the same or parallel mechanisms to regulate Yorkie activity. Here, we dissect how loss of AJ and basolateral components affects Hippo signaling in Drosophila. Surprisingly, while scrib knock-down tissue displays increased reporter activity autonomously, α-cat knock-down tissue shows a cell autonomous decrease and a cell non-autonomous increase of Hippo reporter activity. We provided several lines of evidence to show the differential regulation in polarity protein localizations and oncogenic cooperative overgrowth by AJs and basolateral complexes. Finally, we show that Hippo pathway activity is induced in α-cat and scrib double knocked-down tissue. Taken together, our results provide evidence to show that basolateral modules and AJs act in parallel to modulate Hippo pathway activity. Non-muscle myosin II is an actomyosin component that interacts with the actin. Non-muscle myosin II also interacts with lgl, though the function of this interaction is not clear. Our lab demonstrated that modulating F-actin regulates Hippo pathway activity, and lgl also has been described as a Hippo pathway regulator. Therefore we suspect that myosin II is also involved in Hippo pathway regulation. We first characterized non-muscle Myosin II as a novel tumor suppressor gene by affecting Hippo pathway activity. Upstream regulators of Myosin II, members in the Rho signaling pathway, also displayed similar phenotypes as the Myosin II knock-down tissues. Apoptosis is also induced in myosin II knock-down tissues, however, blocking cell death does not affect myosin II knock-down induced Hippo activation. Our data suggested hyperactivating myosin II induced F-actin accumulation so therefore induces Hippo target activation. Unexpectedly, we also observed that reducing F-actin activity induced Hippo target activation in vivo. These controversial data indicated that actomyosin may regulate the Hippo pathway through multiple mechanisms.

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Se desarrollan varias técnicas basadas en descomposición ortogonal propia (DOP) local y proyección de tipo Galerkin para acelerar la integración numérica de problemas de evolución, de tipo parabólico, no lineales. Las ideas y métodos que se presentan conllevan un nuevo enfoque para la modelización de tipo DOP, que combina intervalos temporales cortos en que se usa un esquema numérico estándard con otros intervalos temporales en que se utilizan los sistemas de tipo Galerkin que resultan de proyectar las ecuaciones de evolución sobre la variedad lineal generada por los modos DOP, obtenidos a partir de instantáneas calculadas en los intervalos donde actúa el código numérico. La variedad DOP se construye completamente en el primer intervalo, pero solamente se actualiza en los demás intervalos según las dinámicas de la solución, aumentando de este modo la eficiencia del modelo de orden reducido resultante. Además, se aprovechan algunas propiedades asociadas a la dependencia débil de los modos DOP tanto en la variable temporal como en los posibles parámetros de que pueda depender el problema. De esta forma, se aumentan la flexibilidad y la eficiencia computacional del proceso. La aplicación de los métodos resultantes es muy prometedora, tanto en la simulación de transitorios en flujos laminares como en la construcción de diagramas de bifurcación en sistemas dependientes de parámetros. Las ideas y los algoritmos desarrollados en la tesis se ilustran en dos problemas test, la ecuación unidimensional compleja de Ginzburg-Landau y el problema bidimensional no estacionario de la cavidad. Abstract Various ideas and methods involving local proper orthogonal decomposition (POD) and Galerkin projection are presented aiming at accelerating the numerical integration of nonlinear time dependent parabolic problems. The proposed methods come from a new approach to the POD-based model reduction procedures, which combines short runs with a given numerical solver and a reduced order model constructed by expanding the solution of the problem into appropriate POD modes, which span a POD manifold, and Galerkin projecting some evolution equations onto that linear manifold. The POD manifold is completely constructed from the outset, but only updated as time proceeds according to the dynamics, which yields an adaptive and flexible procedure. In addition, some properties concerning the weak dependence of the POD modes on time and possible parameters in the problem are exploited in order to increase the flexibility and efficiency of the low dimensional model computation. Application of the developed techniques to the approximation of transients in laminar fluid flows and the simulation of attractors in bifurcation problems shows very promising results. The test problems considered to illustrate the various ideas and check the performance of the algorithms are the onedimensional complex Ginzburg-Landau equation and the two-dimensional unsteady liddriven cavity problem.

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We have investigated physical distances and directions of transposition of the maize transposable element Ac in Arabidopsis thaliana. We prepared a transferred DNA (T-DNA) construct that carried a non-autonomous derivative of Ac with a site for cleavage by endonuclease I-SceI (designated dAc-I-RS element). Another cleavage site was also introduced into the T-DNA region outside dAc-I-RS. Three transgenic Arabidopsis plants were generated, each of which had a single copy of the T-DNA at a different chromosomal location. These transgenic plants were crossed with the Arabidopsis that carried the gene for Ac transposase and progeny in which dAc-I-RS had been transposed were isolated. After digestion of the genomic DNA of these progeny with endonuclease I-SceI, sizes of segment of DNA were determined by pulse-field gel electrophoresis. We also performed linkage analysis for the transposed elements and sites of mutations near the elements. Our results showed that 50% of all transposition events had occurred within 1,700 kb on the same chromosome, with 35% within 200 kb, and that the elements transposed in both directions on the chromosome with roughly equal probability. The data thus indicate that the Ac–Ds system is most useful for tagging of genes that are present within 200 kb of the chromosomal site of Ac in Arabidopsis. In addition, determination of the precise localization of the transposed dAc-I-RS element should definitely assist in map-based cloning of genes around insertion sites.