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A linear recursive scheme associated with the love equation

Le Thi Phuong Ngoc , Nguyen Tuan Duy , $icon-email$ Nguyen Thanh Long

Abstract

This paper shows the existence of a unique weak solution of the following Dirichlet problem for a nonlinear Love equation ${\begin{aligned} u_{t t} - u_{x x} - ε u_{x x t t} = f (x, t, u, u_{x}, u_{t}, u_{x t}), 0 < x < L, 0 < t < T, \\ u (0, t) = u (L, t) = 0, \\ u (x, 0) = {\tilde{u}}_{0} (x), u_{t} (x, 0) = {\tilde{u}}_{1} (x), \end{aligned}$ where $ε > 0$ is a constant and ${\tilde{u}}_{0}, {\tilde{u}}_{1}, f$ 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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A linear recursive scheme associated with the love equation

Abstract