Abstract
We consider the Dirichlet–Neumann problem and the spatially periodic Cauchy problem for a nonlinear hyperbolic system with damping and diffusion introduced in [13] for the study of chaos. Firstly, the existence and uniqueness of global solutions with large initial data is established. Then the zero diffusion limits are justified. Moreover, the $ L^2 $ convergence rate in terms of the diffusion coefficient is obtained. Based on a new observation of the structure of the system, two equalities are found to show the existence of global large solutions of the system.
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