Bates, Peter W.; Chen, Fengxin; Wang, Junping Global existence and uniqueness of solutions to a nonlocal phase-field system. (English) Zbl 0938.35035 Bates, P. W. (ed.) et al., Proceedings of the US-Chinese conference: Differential equations and applications, Hangzhou, China, June 24-29, 1996. Cambridge, MA: International Press. 14-21 (1997). In this paper is proved that, under the assumptions \(j\in C^1 (\mathbb{R})\), \(j(s)=j(-s)\geq 0\) \(\forall s\in\mathbb{R}\), and \(\int_\mathbb{R} j=1\); \(f( \varphi)=\varphi-\varphi^3\); \(\varphi_0\in H^1(\mathbb{R})\) and \(\theta_0\in L^2 (\mathbb{R})\), the following nonlocal phase-field system \[ \varphi_t=j*\varphi-\varphi+ f(\varphi)+\ell\theta, \quad \theta_t+ \ell\varphi_t =\Delta\theta, \quad \varphi(0)= \varphi_0,\;\theta(0) =\theta_0 \] has a unique global solution in an appropriate space.For the entire collection see [Zbl 0913.00035]. Reviewer: Costică Moroşanu (Iaşi) Cited in 1 ReviewCited in 7 Documents MSC: 35G25 Initial value problems for nonlinear higher-order PDEs 76T99 Multiphase and multicomponent flows 45K05 Integro-partial differential equations Keywords:nonlinear evolution equations; two-phase flows PDFBibTeX XMLCite \textit{P. W. Bates} et al., in: Proceedings of the US-Chinese conference: Differential equations and applications, Hangzhou, China, June 24--29, 1996. Cambridge, MA: International Press. 14--21 (1997; Zbl 0938.35035)