Abstract

This paper shows the existence of a unique weak solution of the following Dirichlet problem for a nonlinear Love equation ⎧⎩⎨⎪⎪utt−uxx−εuxxtt=f(x,t,u,ux,ut,uxt),0<x<L, 0<t<T,u(0,t)=u(L,t)=0,u(x,0)=u~0(x),ut(x,0)=u~1(x), where ε>0 is a constant and u~0, u~1, f are given functions. This is done by combining the linearization method for a nonlinear term, the Faedo–Galerkin method and the weak compactness method.