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Global Existence, Decay, and Blow up of Solutions of a Singular Nonlocal Viscoelastic Problem

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Abstract

In this work we consider a nonlinear hyperbolic one-dimensional viscoelastic nonlocal problem with a nonlocal boundary condition. We establish a blow up result for large initial data and a decay result for small enough initial data.

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Authors and Affiliations

  1. Department of Mathematics, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Said Mesloub

  2. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Salim A. Messaoudi

Authors
  1. Said Mesloub
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  2. Salim A. Messaoudi
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Correspondence to Said Mesloub.

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Mesloub, S., Messaoudi, S.A. Global Existence, Decay, and Blow up of Solutions of a Singular Nonlocal Viscoelastic Problem. Acta Appl Math 110, 705–724 (2010). https://doi.org/10.1007/s10440-009-9469-6

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  • DOI: https://doi.org/10.1007/s10440-009-9469-6

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