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Eigensolutions in boundary-layer flow adjacent to a stretching wall. (English) Zbl 0619.76011

We present an investigation into the eigensolutions for a one-parameter family of boundary-layer solutions corresponding to a stretching wall. Such stretching boundaries occur in the manufacture of polymer sheeting as well as in other real situations. Analytical results are obtained which give certain of the eigenvalues and eigenfunctions for those two parameter values for which the boundary-layer equations possess an analytical solution. In addition to other particular results found we highlight a remarkable property of this class of boundary-layer flows: viz. that the first eigenvalue can be found analytically for all parameter values for which the boundary-layer solution exists. In all cases the eigensolution is found to represent a disturbance which decays in an appropriate region of the flow field. The results of a complementary numerical study of the eigenvalue problem are also given.

MSC:

76A10 Viscoelastic fluids
35P15 Estimates of eigenvalues in context of PDEs
76M99 Basic methods in fluid mechanics
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