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Original scientific paper

A priori estimates for finite-energy sequences of one-dimensional Cahn-Hilliard functional with non-standard multi-well potential

Andrija Raguž orcid id orcid.org/0000-0001-8045-9636 ; Department of Economics and Mathematics, Zagreb School of Economics and Management, Zagreb, Croatia *

* Corresponding author.


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Abstract

In this paper we provide some results pertaining to asymptotic behaviour as $\varepsilon\str 0$ of the finite-energy sequences of the one-dimensional Cahn-Hilliard functional
\(I^{\varepsilon}_0(u)=\int_{0}^{1}\Big({\varepsilon}^2u'^2(s)+W(u(s))\Big)ds,\)
where \(u\in {\rm H}^{1}\oi{0}{1}\) and where W is a multi-well potential endowed with a non-standard integrability condition. We introduce a new class of finite-energy sequences, we recover its underlying geometric properties as \(\vrepsilon\str 0\), and obtain the related a priori estimates.

Keywords

asymptotic analysis; singular perturbation; Young measures; Cahn-Hiliard functional; regularity

Hrčak ID:

315319

URI

https://hrcak.srce.hr/315319

Publication date:

19.3.2024.

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