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Chaotic oscillations of linear hyperbolic PDE with variable coefficients and implicit boundary conditions

  • * Corresponding author: Qigui Yang

    * Corresponding author: Qigui Yang 
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  • In this paper, the chaotic oscillations of the initial-boundary value problem of linear hyperbolic partial differential equation (PDE) with variable coefficients are investigated, where both ends of boundary conditions are nonlinear implicit boundary conditions (IBCs). It separately considers that IBCs can be expressed by general nonlinear boundary conditions (NBCs) and cannot be expressed by explicit boundary conditions (EBCs). Finally, numerical examples verify the effectiveness of theoretical prediction.

    Mathematics Subject Classification: Primary: 34C28, 35L70; Secondary: 35L05.

    Citation:

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  • Figure 1.  The spatiotemporal profiles of system (23) with $ (\alpha_1,\beta_1) = (0.1,1) $, $ (\alpha_2,\beta_2) = (0.5,1) $, $ x\in [0,1] $ and $ t\in [60,64] $: (a) $ w_{x}(x,t) $; (b) $ w_{t}(x,t) $.

    Figure 2.  The spatiotemporal profiles of system (23) with $ \gamma_1 = 1.1\pi $ and $ \gamma_2 = 0.4\pi $, $ x\in [0,1] $ and $ t\in [60,64] $: (a) $ w_{x}(x,t) $; (b) $ w_{t}(x,t) $.

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