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.
Citation: Xiaoqiang Dai, Wenke Li. Non-global solution for visco-elastic dynamical system with nonlinear source term in control problem[J]. Electronic Research Archive, 2021, 29(6): 4087-4098. doi: 10.3934/era.2021073
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.
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