Controle na fronteira para um sistema de equações de ondas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Uma introdução ao estudo de fibrados vetoriais

Pós-graduação em Matemática Universitária - IGCE

Approximate controllability for the semilinear heat equation in RN involving gradient terms

We prove the approximate controllability of the semilinear heat equation in R^N, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient Ñu. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings, we work with the similarity variables and use weighted Sobolev spaces.

Homotopias e aplicações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Die Faktorisierungsmethode für die elektrische Impedanztomographie im Halbraum

In der vorliegenden Arbeit wird die Faktorisierungsmethode zur Erkennung von Inhomogenitäten der Leitfähigkeit in der elektrischen Impedanztomographie auf unbeschränkten Gebieten - speziell der Halbebene bzw. dem Halbraum - untersucht. Als Lösungsräume für das direkte Problem, d.h. die Bestimmung des elektrischen Potentials zu vorgegebener Leitfähigkeit und zu vorgegebenem Randstrom, führen wir gewichtete Sobolev-Räume ein. In diesen wird die Existenz von schwachen Lösungen des direkten Problems gezeigt und die Gültigkeit einer Integraldarstellung für die Lösung der Laplace-Gleichung, die man bei homogener Leitfähigkeit erhält, bewiesen. Mittels der Faktorisierungsmethode geben wir eine explizite Charakterisierung von Einschlüssen an, die gegenüber dem Hintergrund eine sprunghaft erhöhte oder erniedrigte Leitfähigkeit haben. Damit ist zugleich für diese Klasse von Leitfähigkeiten die eindeutige Rekonstruierbarkeit der Einschlüsse bei Kenntnis der lokalen Neumann-Dirichlet-Abbildung gezeigt. Die mittels der Faktorisierungsmethode erhaltene Charakterisierung der Einschlüsse haben wir in ein numerisches Verfahren umgesetzt und sowohl im zwei- als auch im dreidimensionalen Fall mit simulierten, teilweise gestörten Daten getestet. Im Gegensatz zu anderen bekannten Rekonstruktionsverfahren benötigt das hier vorgestellte keine Vorabinformation über Anzahl und Form der Einschlüsse und hat als nicht-iteratives Verfahren einen vergleichsweise geringen Rechenaufwand.

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

Lp Microlocal Properties for Multi-Quasi-Elliptic Pseudodifferential Operators

2010 Mathematics Subject Classification: Primary 35S05; Secondary 35A17.

Crack Theory with Singularities at the Boundary

2002 Mathematics Subject Classification: 35S15, 35J70, 35J40, 38J40

Generalized Backscattering and the Lax-Phillips Transform

2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.

Solutions Globales Régulières pour Quelques Équations Lineaires D'évolution du Type Pseudo-Différentiel Singulier

2000 Mathematics Subject Classification: 35C15, 35D05, 35D10, 35S10, 35S99.

Second-order elliptic PDE with discontinuous boundary data

We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.

Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups.

We work with Besov spaces Bp,q0,b defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent b. We characterize Bp,q0,b by means of Fourier-analytical decompositions, wavelets and semi-groups. We also compare those results with the well-known characterizations for classical Besov spaces Bp,qs.

'Dripping sweat: sub-tropical spaces in recent Brisbane fiction'

This paper considers the literary landscape of contemporary Brisbane and pays particular attention to the relationship between sub-tropical spaces (homes, streets, and clubs) and local writing. ‘Dripping Sweat’ proposes that within the new urban cool of Brisbane’s cultural life there is nostalgia for the sub-tropical environment that continues to intrude on contemporary fiction. The paper considers the architecture of both public and private spaces and discusses how the literary imagination re-designs contemporary Brisbane with a selective appropriation of environmental settings.

Identifying opportunity spaces for design research in South America: Working with grassroots and community groups

As design research continues to gain momentum in South America, design researchers and practitioners in the region have begun to consider how to the field may address regionally-specific issues, including on-going political struggles. By bringing approaches such as Participatory Design and Adversarial Design that consider political aspects of design, local researchers have explored various forms that these two approaches could take that are tailored to the needs and values of different communities across the region. This paper focuses on identifying opportunities for developing design research projects in community-based and grassroots-oriented contexts. The paper presents the findings of our study about the understanding and experience of design researchers and experts who have been working closely with community groups and grassroots organisations in South America. Five themes emerged, highlighting opportunities and challenges related to positioning contemporary design research in the region, integration of adversarial perspectives into design processes, leveraging local obstacles through creativity, and the potential of building capacity within community groups and grassroots organisations for sustainability and autonomy.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.