Khaled Zennir, Salah Boulaaras, Bahri Cherif, Ali Allahem, New Mathematical Studies for Surface Waves on Multi-Layered Liquid Films, Research Journal of Applied Sciences, Volume 14,Issue 2, 2019, Pages 61-66, ISSN 1815-932x, rjasci.2019.61.66, (https://makhillpublications.co/view-article.php?doi=rjasci.2019.61.66) Abstract: We consider a coupled system of mathematical problem given in the form of two partial differential equations in viscoelasticities describing the propagation of surface waves on multi-layered liquid films. We establish the existence of solutions for initial-value problem (1.3) in the linear case by using a priori energy estimates. Keywords: Surface waves;existence;multi-layered liquid film;infinite memory;mathematical problem;viscoelasticities