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Chaotic oscillations of a linear hyperbolic PDE with a general nonlinear boundary condition. (English) Zbl 1437.35448

Summary: This article establishes a theorem that guarantees the occurrence of chaotic oscillations in a system governed by a linear hyperbolic partial differential equation (PDE) with a nonlinear boundary condition (NBC). Compared with the NBCs in all previous related literature, such an NBC is more general. Both the left end and the right end of the system parameter interval for the occurrence of chaotic oscillations are precisely characterized. The chaotic results obtained are further applied to two specific NBCs and the telegraph equation. Finally, numerical examples verify the effectiveness of theoretical prediction.

MSC:

35L20 Initial-boundary value problems for second-order hyperbolic equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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