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Existence and Decay of Solutions of a Mixed Nonlocal Problem

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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.

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Acknowledgements

The authors wish to express their sincere thanks to the referees and the editor for their valuable comments. This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under Grant no. B2013-18-05.

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Correspondence to Nguyen Thanh Long.

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Dr. Nguyen Thanh Long was a session invited speaker at the Vietnam Congress of Mathematicians 2013.

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Phuong Ngoc, L.T., Triet, N.A. & Long, N.T. Existence and Decay of Solutions of a Mixed Nonlocal Problem. Vietnam J. Math. 44, 273–293 (2016). https://doi.org/10.1007/s10013-015-0158-7

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

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