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Nonisotropic spatiotemporal chaotic vibrations of the one-dimensional wave equation with a mixing transport term and general nonlinear boundary condition. (English) Zbl 1314.35070

Summary: Nonisotropic spatiotemporal chaotic vibrations can happen for a linear wave equation with a mixing transport term on the unit interval and with a nonlinear van der Pol boundary condition at one end when the parameter(s) enters some regime [G. Chen et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 3, 535–559 (2002; Zbl 1044.37019)]. In this paper, on the one hand, the equation with general nonlinear boundary conditions is considered. On the other hand, parameter range for the route to chaos is more precisely classified. The results obtained here generalize and sharpen those both in the above paper and the earlier work of [The first and the third author, J. Math. Anal. Appl. 361, No. 1, 69–85 (2010; Zbl 1183.35189)]. Two examples and their corresponding numerical simulations of chaotic space-time profiles are also illustrated.{
©2010 American Institute of Physics}

MSC:

35L05 Wave equation
35J65 Nonlinear boundary value problems for linear elliptic equations
34B15 Nonlinear boundary value problems for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
76F25 Turbulent transport, mixing
68U20 Simulation (MSC2010)
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