Displaying similar documents to “On the circle criterion for boundary control systems in factor form: Lyapunov stability and Lur'e equations”

Asymmetric heteroclinic double layers

Michelle Schatzman (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Let be a non-negative function of class C from 2 to , which vanishes exactly at two points and . Let (, ) be the set of functions of a real variable which tend to at -∞ and to at +∞ and whose one dimensional energy E 1 ( v ) = ∫ W ( v ) + | v ' | 2 / 2 x is finite. Assume that there exist two isolated minimizers and of the energy over (, ). Under a mild coercivity condition on the potential and a generic spectral condition on the linearization...

Anisotropic functions: a genericity result with crystallographic implications

Victor J. Mizel, Alexander J. Zaslavski (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In the 1950's and 1960's surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was . By examining step/terrace () surface defects it was discovered through lengthy and tedious experiments...

Higher-order phase transitions with line-tension effect

Bernardo Galvão-Sousa (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [Ann. Inst. Henri Poincaré, Anal. non linéaire 4 (1987) 487–512], and in a different form by...