Global Existence, Decay, and Blow‐Up of Solutions of a Singular Nonlocal Viscoelastic System With a Nonlinear Damping Term, Nonlocal Boundary Condition, and Variable Exponents

ABSTRACT In this study, we consider the existence of a global solution, general decay result of a nonlinear singular viscoelastic equation with a nonlocal boundary condition, nonlinear source term, and nonlinear damping term with variable exponent. Furthermore, we prove the blow‐up result with the Georgiev and Todorova method for the positive and nonpositive initial energy in the case where the damping term is nonlinear.