RESULT OF LOCAL EXISTENCE OF SOLUTIONS OF NONLOCAL VISCOELASTIC SYSTEM WITH RESPECT TO THE NONLINEARITY OF SOURCE TERMS

This work deals with the proof of local existence theorem of solutions for coupled nonlocal singular viscoelastic system with respect to the nonlinearity of source terms by using the Faedo–Galerkin method together with energy methods. This work makes a new contribution, since most of the previous works did not address the proof of the theorem of the local existence of solutions. It is also a completed study of Boulaaras et al. [Adv. Differ. Equ. 2020 (2020) 310].