BLOW-UP OF SOLUTIONS TO A NONLINEAR WAVE EQUATION WITH A TIME DELAY
CONDITION OF FRACTIONAL TYPE AND LOGARITHMIC NONLINEARITY
- Aounallah Radhouane
, - Benaissa Abbès,
- Zarai Abderrahmane
Aounallah Radhouane
Djillali Liabès University , of Mathematics B. P 89 Sidi Bel Abbès 22000, Algeria
Corresponding Author:radhouaneaounallah@gmail.com
Author ProfileZarai Abderrahmane
University of Larbi Tebessi, Tebessa,Algeria
Author ProfileAbstract
In the present work, we consider a nonlinear wave equation with a time
delay condition of fractional type and a logarithmic source. Using the
semigroup theory, we get the existence of a local weak solution.
Moreover, we show that this solution blows up in finite time with
negative initial-energy.
