Topics on Concentration Phenomena and Problems with Multiple Scales

1. Auflage 2006
ISBN: 978-3-540-36241-8
Verlag: Springer

Buch, Englisch, Band 2, 316 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1030 g

Reihe: Lecture Notes of the Unione Matematica Italiana

The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena is a challenging topic of very active research. This volume collects lecture notes on the asymptotic analysis of such problems when multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes, and on concentration effects in Ginzburg-Landau energies and in subcritical growth problems.

Zielgruppe

Research

Autoren/Hrsg.

Braides, Andrea

Chiadò Piat, Valeria

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Problems with multiple scales.- From discrete systems to continuous variational problems: an introduction.- Relaxation for bulk and interfacial energies.- Convergence of Dirichlet forms on fractals.- Homogenization in perforated domains.- Homogenization of random non stationary parabolic operators.- Problems with concentration.- ?-convergence for concentration problems.- Gamma-convergence of gradient flows and applications to Ginzburg-Landau vortex dynamics.- PDE analysis of concentrating energies for the Ginzburg-Landau equation.