Non-global solution for visco-elastic dynamical system with nonlinear source term in control problem

Abstract

<p style='text-indent:20px;'>In this paper, we study the initial boundary value problem of the visco-elastic dynamical system with the nonlinear source term in control system. By variational arguments and an improved convexity method, we prove the global nonexistence of solution, and we also give a sharp condition for global existence and nonexistence.</p>