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Topics on Concentration Phenomena and Problems with Multiple Scales
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Artikel-Nr:
9783540365464
Veröffentl:
2006
Einband:
eBook
Seiten:
316
Autor:
Andrea Braides
Serie:
2, Lecture Notes of the Unione Matematica Italiana
eBook Typ:
PDF
eBook Format:
Reflowable eBook
Kopierschutz:
NO DRM
Sprache:
Englisch
Beschreibung:
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.
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.
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.