Izvorni znanstveni članak
A priori estimates for finite-energy sequences of one-dimensional Cahn-Hilliard functional with non-standard multi-well potential
Andrija Raguž
orcid.org/0000-0001-8045-9636
; Department of Economics and Mathematics, Zagreb School of Economics and Management, Zagreb, Croatia
Sažetak
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.
Ključne riječi
asymptotic analysis; singular perturbation; Young measures; Cahn-Hiliard functional; regularity
Hrčak ID:
315319
URI
Datum izdavanja:
19.3.2024.
Posjeta: 63 *