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Global existence and energy decay of solutions for a wave equation with non-constant delay and nonlinear weights

  • Received: 01 January 2020 Revised: 01 February 2020
  • Primary: 35D05, 35E15; Secondary: 35Q35

  • We consider the wave equation with a weak internal damping with non-constant delay and nonlinear weights given by

    utt(x,t)uxx(x,t)+μ1(t)ut(x,t)+μ2(t)ut(x,tτ(t))=0

    in a bounded domain. Under proper conditions on nonlinear weights μ1(t),μ2(t) and non-constant delay τ(t), we prove global existence and estimative the decay rate for the energy.

    Citation: Vanessa Barros, Carlos Nonato, Carlos Raposo. Global existence and energy decay of solutions for a wave equation with non-constant delay and nonlinear weights[J]. Electronic Research Archive, 2020, 28(1): 205-220. doi: 10.3934/era.2020014

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  • We consider the wave equation with a weak internal damping with non-constant delay and nonlinear weights given by

    \begin{eqnarray*} \label{NLS}   u_{tt}(x,t) - u_{xx}(x,t)+\mu_1(t)u_t(x,t) +\mu_2(t)u_t(x,t-\tau(t)) = 0 \end{eqnarray*}\begin{eqnarray*} \label{NLS}   u_{tt}(x,t) - u_{xx}(x,t)+\mu_1(t)u_t(x,t) +\mu_2(t)u_t(x,t-\tau(t)) = 0 \end{eqnarray*}

    in a bounded domain. Under proper conditions on nonlinear weights μ1(t),μ2(t) and non-constant delay τ(t), we prove global existence and estimative the decay rate for the energy.



    A Correction on

    Apomorphine-induced pathway perturbation in MPP+-treated SH-SY5Y cells by

    Jin Hwan Do AIMS Mol Sci, 2017, 4(3): 271-287. DOI: 10.3934/molsci.2017.3.271

    In the original article [1], a reference was missed. Now we add it as reference number [23]:

    Pepe D, Do JH (2016) Comparison of perturbed pathways in two different cell models for Parkinson's disease with structural equation model. J Comput Biol 23: 90-101.

    The error was introduced during production. We apologize for any inconvenience caused to the readers by this change. This error does not change the scientific conclusions of the article in any way. The original manuscript will remain online on the article webpage.




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