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Existence of chaotic oscillations in second-order linear hyperbolic PDEs with implicit boundary conditions. (English) Zbl 1434.35021

Summary: This paper establishes rigorously mathematical theorems that guarantee the existence of chaotic oscillations in the systems of second-order linear hyperbolic PDEs. It separately considers the systems with nonlinear explicit boundary conditions (EBCs) and nonlinear implicit boundary conditions (IBCs) as well as those with such IBCs subjected to small perturbations, where IBCs include EBCs as special cases but the latter cannot in general be expressed by the former. Numerical examples are demonstrated to illustrate the effectiveness of theoretical results.

MSC:

35L05 Wave equation
35L20 Initial-boundary value problems for second-order hyperbolic equations
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