Sci Math | Existence and Decay of Solutions of a Mixed Nonlocal Problem

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Existence and Decay of Solutions of a Mixed Nonlocal Problem

Authors: Nguyễn Anh Triết, Nguyễn Thành Long, Lê Thị Phương Ngọc,

https://doi.org/10.1007/s10013-015-0158-7

Publisher, magazine: ,

Publication year: 2016

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Abstract

In this paper, we consider a mixed nonlocal problem for a wave equation with the Dirichlet condition at x = 1 and a nonlocal boundary condition at x = 0 of integral forms. First, we establish two local existence theorems by using Faedo–Galerkin method. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions.

Tags: Faedo–Galerkin method; Nonlinear wave equation; Local existence; Global existence; Exponential decay

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