Izvorni znanstveni članak

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

Preuzmi JATS datoteku

Sažetak

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.

Ključne riječi

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

Hrčak ID:

318144

URI

https://hrcak.srce.hr/318144

Datum izdavanja:

24.11.2024.

Posjeta: 273 *