Sökning: "Multiscale convergence"
Visar resultat 1 - 5 av 25 avhandlingar innehållade orden Multiscale convergence.
Sammanfattning : The main focus of the present thesis is on the homogenization of some selected elliptic and parabolic problems. More precisely, we homogenize: non-periodic linear elliptic problems in two dimensions exhibiting a homothetic scaling property; two types of evolution-multiscale linear parabolic problems, one having two spatial and two temporal microscopic scales where the latter ones are given in terms of a two-parameter family, and one having two spatial and three temporal microscopic scales that are fixed power functions; and, finally, evolution-multiscale monotone parabolic problems with one spatial and an arbitrary number of temporal microscopic scales that are not restricted to be given in terms of power functions. LÄS MER
2. Homogenization of Some Selected Elliptic and Parabolic Problems Employing Suitable Generalized Modes of Two-Scale Convergence
Sammanfattning : The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. Since homogenization is defined in terms of H-convergence, we desire to find the H-limits of sequences of periodic monotone parabolic operators with two spatial scales and an arbitrary number of temporal scales and the H-limits of sequences of two-dimensional possibly non-periodic linear elliptic operators by utilizing the theories for evolution-multiscale convergence and λ-scale convergence, respectively, which are generalizations of the classical two-scale convergence mode and custom-made to treat homogenization problems of the prescribed kinds. LÄS MER
Sammanfattning : This thesis mainly deals with questions concerning the convergence of some sequences of elliptic and parabolic linear and non-linear operators by means of G-convergence and homogenization. In particular, we study operators with oscillations in several spatial and temporal scales. LÄS MER
Sammanfattning : This thesis deals with questions concerning the convergence of sequences of functions and operators. G-convergence is studied for elliptic and parabolic equations and the necessary investigations of the properties of certain monotone operators are made. LÄS MER
5. Analysis and Applications of the Heterogeneous Multiscale Methods for Multiscale Elliptic and Hyperbolic Partial Differential Equations
Sammanfattning : This thesis concerns the applications and analysis of the Heterogeneous Multiscale methods (HMM) for Multiscale Elliptic and Hyperbolic Partial Differential Equations. We have gathered the main contributions in two papers. LÄS MER