Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions

Le Thi Phuong Ngoc; Nguyen Thanh Long

doi:10.3934/cpaa.2013.12.2001

Article Contents

2013, Volume 12, Issue 5: 2001-2029. Doi: 10.3934/cpaa.2013.12.2001

This issue Previous Article Multiplicity of solutions for Neumann problems with an indefinite and unbounded potential Next Article Asymptotically periodic solutions of neutral partial differential equations with infinite delay

Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions

Le Thi Phuong Ngoc^1, and
Nguyen Thanh Long^2,

1.
Nha Trang Educational College, 01 Nguyen Chanh Str., Nha Trang City
2.
Department of Mathematics and Computer Science, University of Natural Science, Vietnam National University Ho Chi Minh City, 227 Nguyen Van Cu Str., Dist.5, Ho Chi Minh City

Received: December 31, 2011

Revised: October 31, 2012

Published: August 2013

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Abstract

The paper is devoted to the study of a nonlinear wave equation with nonlocal boundary conditions 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.

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Mathematics Subject Classification: 35L05, 35L15, 35L70, 37B25.

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