We study the properties of the minimizers of a singularly perturbed non-convex functional with a penalization term Fε,μ(v,u;I)=1/2ε2∫Ivxx2dx+1/2∫IW(vx)dx+μ/2ε2∫I(v-u)2dx, where I=(0, 1), 0 < ε « 1 and μ > 0 are parameters, u is a given function and W(p)=(p2-1)2. We analyze the phenomenon of microstructure formation and show the dependence on μ and u.
Analysis of microstructure of a non-convex functional with penalization term / Colucci, Renato. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 388:1(2012), pp. 370-385. [10.1016/j.jmaa.2011.09.056]
Analysis of microstructure of a non-convex functional with penalization term
Colucci, Renato
2012-01-01
Abstract
We study the properties of the minimizers of a singularly perturbed non-convex functional with a penalization term Fε,μ(v,u;I)=1/2ε2∫Ivxx2dx+1/2∫IW(vx)dx+μ/2ε2∫I(v-u)2dx, where I=(0, 1), 0 < ε « 1 and μ > 0 are parameters, u is a given function and W(p)=(p2-1)2. We analyze the phenomenon of microstructure formation and show the dependence on μ and u.File in questo prodotto:
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