English

Stationary layered solutions for a system of Allen-Cahn type equations

Analysis of PDEs 2014-04-22 v2

Abstract

We consider a class of semilinear elliptic system of the form Δu(x,y)+W(u(x,y))=0,(x,y)R2-\Delta u(x,y)+\nabla W(u(x,y))=0,\quad (x,y)\in\R^{2} where W:R2RW:\R^{2}\to\R is a double well non negative symmetric potential. We show, via variational methods, that if the set of solutions to the one dimensional system q¨(x)+W(q(x))=0, xR-\ddot q(x)+\nabla W(q(x))=0,\ x\in\R, which connect the two minima of WW as x±x\to\pm\infty has a discrete structure, then the given system has infinitely many layered solutions.

Keywords

Cite

@article{arxiv.1211.5751,
  title  = {Stationary layered solutions for a system of Allen-Cahn type equations},
  author = {Francesca Alessio},
  journal= {arXiv preprint arXiv:1211.5751},
  year   = {2014}
}