Complete WKB asymptotics of high frequency vibrations in a stiff problem - Mathematics > Spectral TheoryReport as inadecuate




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Abstract: Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem isdescribed in the case of the fourth-order ordinary differential operator.Considering the stiffness coefficient that depends on a small parameter epsilonand vanishes as epsilon tends to zero on a subinterval, we prove the existenceof low and high frequency resonance vibrations. The low frequency vibrationsadmit the power series expansions on epsilon but this method is not applicableto the description of high frequency vibrations. However, the nonclassicalasymptotics on epsilon of the high frequency vibrations were constructed usingthe WKB method.



Author: N. Babych, Yu. Golovaty

Source: https://arxiv.org/







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