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    STUDIA MATHEMATICA - Issue no. 1 / 2023  
         
  Article:   LOCAL EXISTENCE AND BLOW UP OF SOLUTIONS TO A LOGARITHMIC NONLINEAR WAVE EQUATION WITH TIME-VARYING DELAY.

Authors:  ABDELBAKI CHOUCHA, DJAMEL OUCHENANE.
 
       
         
  Abstract:   DOI: 10.24193/subbmath.2023.1.13

Published Online: 2023-03-20
Published Print: 2023-04-30
pp. 171-187

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In this work, we are concerned with a problem of a logarithmic nonlinear wave equation with time-varying delay term. We established the local existence result and we proved a blow up result for the solution with negative initial energy under suitable conditions. This improves earlier results in the literature [11] for time-varying delay.

Mathematics Subject Classification (2010): 35B05, 35B40, 35Q99, 73C99.

Keywords: Wave equation, blow up, logarithmic source, varying delay term.
 
         
     
         
         
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