On the Singular Limit for a Cass of Problems Modelling Phase Transitions
1987; Society for Industrial and Applied Mathematics; Volume: 18; Issue: 5 Linguagem: Inglês
10.1137/0518105
ISSN1095-7154
AutoresNicholas D. Alikakos, K. C. Shaing,
Tópico(s)Advanced Mathematical Modeling in Engineering
ResumoThe total variation is a measure of the complexity of a given solution to ${{(\varepsilon )} \mathord{\left/ {\vphantom {{(\varepsilon )} {\varepsilon ^2 u''_\varepsilon }}} \right. \kern-\nulldelimiterspace} {\varepsilon ^2 u''_\varepsilon }} - f(x,u_\varepsilon ) = 0$. For stable solutions, under appropriate conditions on f, the total variation can be bounded uniformly in $\varepsilon $. This estimate provides sufficient compactness for relating the stable solutions of $(\varepsilon )$ to those of the limiting equation $(\varepsilon = 0)$.
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