Original scientific paper

https://doi.org/10.3336/gm.59.1.06

Some results in asymptotic analysis of finite-energy sequences of one-dimensional Cahn–Hilliard functional with non-standard two-well potential

Andrija Raguž orcid.org/0000-0001-8045-9636 ; Department of Economics and Mathematics, Zagreb School of Economics and Management, Filipa Vukasovića 1, 10 000 Zagreb, Croatia

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Abstract

In this paper we extend the consideration of G. Leoni
pertaining to the finite-energy sequences of the one-dimensional
Cahn-Hilliard functional
\[
I^{\varepsilon}_0(u)=\int_{0}^{1}\Big({\varepsilon}^2
u'^2(s)+W(u(s))\Big)ds,
\]
where \(u\in {\rm H}^{1}(0,1)\) and where \(W\) is a two-well
potential with symmetrically placed wells endowed with a
non-standard integrability condition. We introduce several new
classes of finite-energy sequences, we recover their underlying geometric properties as
\(\varepsilon\longrightarrow 0\), and we prove the related compactness result.

Keywords

Asymptotic analysis, singular perturbation, Young measures, Cahn-Hilliard functional, compactness

Hrčak ID:

318144

URI

https://hrcak.srce.hr/318144

Publication date:

28.6.2024.

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