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A linear recursive scheme associated with the love equation
Le Thi Phuong Ngoc, Nguyen Tuan Duy, Nguyen Thanh Long

 

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.

 

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