Abstract
In this paper, we consider an abstract second-order viscoelastic equation with infinite memory, time-varying delay and a nonlinear source term. To the best of our knowledge, there is no blow-up result of solutions for the nonlinear viscoelastic equation with time-varying delay. Moreover, our result extends the blow-up result obtained for problems without memory term to those with infinite memory and problems with constant delay to time-varying delay. Under suitable conditions on initial data, the kernel memory function and the involved functionals, we establish the local existence using the semigroup theory and we prove a finite time blow-up result for the solution with positive initial energy. We also give some applications to illustrate our main result.
Acknowledgements
The authors are highly grateful to the anonymous referee for his/her valuable comments and suggestions for the improvement of the paper. This research work is supported by the General Direction of Scientific Research and Technological Development (DGRSDT), Algeria.
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Correction Statement
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