Attractors of a nonlinear boundary value problem arising in aeroelasticity

The statement of nonlinear aeroelasticity problems can be found in [1, 2]. Related mathematical problems usually involve a generalization of the Andronov-Hopf bifurcation theorem or its analogs to the corresponding classes of differential equations [2-5]. Specific applications of these mathematical results are rather laborious even for the simplest flutter problems (e.g., see [2-6]). Here one often uses the Galerkin method, and the accuracy of numerical results is not alu always satisfactory. Bolotin [1, pp. 286-289] suggested a model boundary value problem in which one call find time-periodic solutions without resorting to the Andronov-Hopf theorem. He also indicated some periodic solutions in the form of a traveling wave. We return to this nonlinear boundary value problem for several reasons. First, we;analyze the stability of the solutions given in [1]. Second, we find other periodic solutions. Finally, we show that under certain conditions on the coefficients, the boundary value problem call have a three-dimensional attractor filled by a continuum of periodic solutions.