Absolute Continuity of Solutions to Reaction-Diffusion Equations with Multiplicative Noise

We prove absolute continuity of the law of the solution, evaluated at fixed points in time and space, to a parabolic dissipative stochastic PDE on L (G), where G is an open bounded domain in ℝ with smooth boundary. The equation is driven by a multiplicative Wiener noise and the nonlinear drift term is the superposition operator associated to a real function that is assumed to be monotone, locally Lipschitz continuous, and growing not faster than a polynomial. The proof, which uses arguments of the Malliavin calculus, crucially relies on the well-posedness theory in the mild sense for stochastic evolution equations in Banach spaces. 2

Non elliptic SPDEs and ambit fields: existence of densities

Relying on the method developed in [debusscheromito2014], we prove the existence of a density for two different examples of random fields indexed by (t,x)\in(0,T]\times \Rd. The first example consists of SPDEs with Lipschitz continuous coefficients driven by a Gaussian noise white in time and with a stationary spatial covariance, in the setting of [dalang1999]. The density exists on the set where the nonlinearity $\sigma$ of the noise does not vanish. This complements the results in [sanzsuess2015] where $\sigma$ is assumed to be bounded away from zero. The second example is an ambit field with a stochastic integral term having as integrator a L\'evy basis of pure-jump, stable-like type.Comment: 23 page

Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation

Nonlinear stochastic evolution equations of second order with damping

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with an internal approximation. Uniqueness is proved as well.Comment: This is the version of the article accepted for publication. The final publication is available at http://link.springer.co

Teacher’s formation: Between the “aestheticization” that affirms life, as it is, and the “rationalization” that denies it

v.13, n. 2, p. 44-65, jul./dez. 2015.Submitted by Marlene Santos ([email protected]) on 2016-03-08T20:38:09Z No. of bitstreams: 1 Artigo - Sergio Pereira da Silva - 2015.pdf: 621391 bytes, checksum: 66a59ca75869be4662c928f019b39196 (MD5)Approved for entry into archive by Claudia Moura ([email protected]) on 2016-03-14T10:38:09Z (GMT) No. of bitstreams: 1 Artigo - Sergio Pereira da Silva - 2015.pdf: 621391 bytes, checksum: 66a59ca75869be4662c928f019b39196 (MD5)Approved for entry into archive by Claudia Moura ([email protected]) on 2016-03-14T10:58:53Z (GMT) No. of bitstreams: 1 Artigo - Sergio Pereira da Silva - 2015.pdf: 621391 bytes, checksum: 66a59ca75869be4662c928f019b39196 (MD5)Made available in DSpace on 2016-03-14T10:58:53Z (GMT). No. of bitstreams: 1 Artigo - Sergio Pereira da Silva - 2015.pdf: 621391 bytes, checksum: 66a59ca75869be4662c928f019b39196 (MD5) Previous issue date: 2015-11-10Programa de Apoio à Publicações Periódicas Científicas (PROAPUPEC) da UFGO autor utiliza o pensamento de Nietzsche e de comentaristas, além de alguns filósofos da educação brasileira, como referências teóricas para analisar o que chamou de “a decadência da formação de professores, no Brasil”. Inicia sua análise no período mítico-trágico dos gregos antigos, época de uma cultura estética e afirmadora da vida e analisa o processo de ruptura, que silencia a cultura trágica e estética e dá voz à cultura racional que emerge, sobretudo com Platão, Paulo de Tarso e Agostinho. Com este último, a “metafísica cristã” se institucionaliza como laudatória do catolicismo em direção a toda Europa medieval, além de outros povos. O autor situa na ruptura mencionada a origem do ressentimento ou da reatividade que são dois fenômenos culturais que fundamentam o que ele chamou “Pedagogia do Ressentimento”, ou seja, um discurso pedagógico reativo, responsável, no entendimento do autor, pela decadência do processo de formação de professores.El autor utiliza Nietzsche y comentaristas, así como filósofos de la educación brasileña, y las referencias teóricas para el análisis de la “decadencia de la formación docente en Brasil”. Parte del período mítico y trágico de los antiguos griegos, el tiempo de una cultura estética y analiza el proceso de ruptura, que silencia la cultura y la estética trágica y da voz a la cultura racional emergente, especialmente con Platón, Pablo de Tarso y Agustín. Con este último, la "metafísica cristiana" está institucionalizada em el catolicismo y em su laudatoria hacia por toda la Europa medieval, y otras naciones. El autor el autor analiza, geneologicamente, el “ resentimiento” o la “reactividad” que son dos fenómenos culturales que subyacen a lo que él llamó "Pedagogía del Resentimiento", es decir, un discurso pedagógico reactivo, piadoso y redentor, responsable, en opinión del autor, por el proceso de descomposición em la educación y em la formación del profesorado.The author uses Nietzsche and commentators, as well as philosophers of Brazilian education, as a theoretical framework to analyze the decay of teacher formation in Brazil. First of all, he analyzes the mythic-tragic period of the ancient Greeks, the time of an aesthetic culture and life-affirming. Then, he describes the process of rupture toward the rational and emerging culture, moment that he emphasizes thinkers as Plato, Paul of Tarsus and Augustine. Thus, the metaphysical-Christian’ culture is institutionalized as Catholicism’s laudatory and reaches all Europe and its colonized peoples. The “resentment” or “reactivity” is located in this breakdown between two cultures and two diferente conceptions of formation, This reactivity created what the author understands as a "Pedagogy of Resentment" and its reactive pedagogical’s discourse which is responsable, according to the author, for the decline of this teacher’s formation in Brazil