A refined description of evolving interfaces in certain nonlinear wave equations (Q1635647)

Central point of the investigation is the semilinear wave equation \[ u_{tt}-{\Delta}u + {\frac{2}{{\epsilon}^2}}({u^2}-1)u=0, \quad 0<\epsilon\ll 1. \] The goal in this article is to improve estimates and existence results obtained in two previous papers of the second author [Anal. PDE 4, No. 2, 285--340 (2011; Zbl 1270.35318); and \textit{B. Galvão-Sousa}, Rend. Circ. Mat. Palermo (2) 64, No. 1, 117--148 (2015; Zbl 1326.35202)].