Thesis (Ph.D.)--Memorial University of Newfoundland, 2004. / Bibliography: leaves 175-182.

Thesis (Ph.D.)--Ohio University, June, 2004. / Title from PDF t.p. Includes bibliographical references (p. 167-171)

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Loukas F. Kallivokas. Vita. Includes bibliographical references.

by Pierre Dersin, Alexander H. Levis. / "August 1982." / Bibliography: leaf [4]. / Support by the Division of Electric Energy System of the U.S. Dept. of Energy under Contract no. AC01-77-ET29033

Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 77-79).

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-01-28Bitstream added on 2014-06-13T20:35:09Z : No. of bitstreams: 1 barros_aap_me_sjrp.pdf: 459604 bytes, checksum: 0a23c4af2e8f9afe3807f0dd603a1237 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo desse trabalho é estudar problemas de valor de contorno com três pontos lineares e não ineares, também conhecidos como problemas não Isto é feito, usando as funções de Green, usadas para resolver problemas de valor de contorno com dois pontos. / The aim of this work is to study boundary value problems with three points also known as non-classical problems. This is done using the Green's functions, which are used to solve two-point boundary value problems.

Enclosure theorems for the eigenvalues and representational formulae for the eigenfunctions of a linear, elliptic, second order partial differential operator will be established for specific domain perturbations to which the classical theory cannot be applied. In particular, the perturbation of n-dimensional Euclidean space E[superscript]n to an n-disk D[subscript]a of radius a is considered in Chapter I and the perturbation of the upper half-space H[superscript]n of E[superscript]n to the upper half of D[subscript]a, S[subscript]a, is discussed in Chapter II. In each case a general self-adjoint boundary condition is adjoined on the bounding surface of the perturbed domain. / Science, Faculty of / Mathematics, Department of / Graduate

No description available.

Nous étendons la théorie des espaces de tentes, définis classiquement sur R^n, à différents espaces métriques. Pour les espaces doublant nous montrons que la théorie usuelle «globale» reste valide, et pour les espaces «non-uniformément localement doublant» (y compris R^n avec la mesure gaussienne) nous établissons une théorie locale satisfaisante. Dans le contexte doublant nous prouvons des résultats de plongement du type Hardy–Littlewood–Sobolev pour des espaces de tentes a poids, et dans le cas particulier des espaces métriques non-bornes AD-réguliers nous identifions les espaces d’interpolation réelle (les «espaces-Z») des espaces de tentes a poids. Les espaces de tentes a poids et les espaces-Z sur R^n sont ensuite utilises pour construire les espaces de Hardy–Sobolev et de Besov adaptes a des opérateurs de Dirac perturbes. Ces espaces jouent un rôle clé dans la classification des solutions de systèmes du premier ordre de type Cauchy–Riemann (ou de manière équivalente, la classification des gradients conormaux des solutions de systèmes elliptiques de second ordre) dans les espaces de tentes à poids et les espaces-Z. Nous établissons cette classification, et en corollaire nous obtenons une classification utile des cas ou les problèmes de Neumann et de Régularité; sont bien poses, pour des systèmes elliptiques de second ordre avec coefficients complexes et données dans les espaces de Hardy–Sobolev et de Besov d’ordre s en (-1,0). / We extend the theory of tent spaces from Euclidean spaces to various types of metric measure spaces. For doubling spaces we show that the usual `global' theory remains valid, and for `non-uniformly locally doubling' spaces (including R^n with the Gaussian measure) we establish a satisfactory local theory. In the doubling context we show that Hardy–Littlewood–Sobolev-type embeddings hold in the scale of weighted tent spaces, and in the special case of unbounded AD-regular metric measure spaces we identify the real interpolants (the `Z-spaces') of weighted tent spaces.Weighted tent spaces and Z-spaces on R^n are used to construct Hardy–Sobolev and Besov spaces adapted to perturbed Dirac operators. These spaces play a key role in the classification of solutions to first-order Cauchy–Riemann systems (or equivalently, the classification of conormal gradients of solutions to second-order elliptic systems) within weighted tent spaces and Z-spaces. We establish this classification, and as a corollary we obtain a useful characterisation of well-posedness of Regularity and Neumann problems for second-order complex-coefficient elliptic systems with boundary data in Hardy--Sobolev and Besov spaces of order s in (-1,0).

In this thesis, we study two stochastic reaction diffusion models - the diffusion limited reaction model of Smoluchowski, and a second approach popularized by Doi. Both models treat molecules as points undergoing Brownian motion. The former represents chemical reactions between two reactants through the use of reactive boundary conditions, with two molecules reacting instantly upon reaching the boundary of a properly embedded open set, termed the reaction region (or more generally some fixed lower dimensional sub-manifold). The Doi model uses reaction potentials, supported in the reaction region, whereby two molecules react with a fixed probability per unit time, λ, upon entering the reaction region. The problem considered is that of obtaining estimates for convergence rates, in λ, of the Doi model to the Smoluchowski model. This problem fits into the theory of singular perturbation or optimization, depending on which reactive boundary conditions one considers, and we solve it - at least for the bimolecular reaction with one stationary target.