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On the decay and global nonexistence of solutions to a damped wave equation with variable-exponent nonlinearity and delay

Volume 122 / 2019

Mohammad Kafini, Salim Messaoudi Annales Polonici Mathematici 122 (2019), 49-70 MSC: 35B35, 35B40, 35L05, 74H35. DOI: 10.4064/ap180524-31-10 Published online: 21 March 2019

Abstract

In this work, we are concerned with a delayed nonlinear wave equation with variable exponents. In the absence of the source term, we prove a decay result, while in the presence of the source term, we prove a global nonexistence result. In addition, in the latter case, the life span time is estimated.

Authors

  • Mohammad KafiniDepartment of Mathematics and Statistics
    KFUPM
    Dhahran 31261, Saudi Arabia
    e-mail
  • Salim MessaoudiDepartment of Mathematics and Statistics
    KFUPM
    Dhahran 31261, Saudi Arabia
    and
    Department of Mathematics
    University of Sharjah
    P.O. Box 27272
    Sharjah, UAE
    e-mail
    e-mail

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