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Zbl 1156.35458
Duruk, N.; Erkip, A.; Erbay, H.A.
A higher-order Boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity. (English)
[J] IMA J. Appl. Math. 74, No. 1, 97-106 (2009). ISSN 0272-4960; ISSN 1464-3634/e

Summary: In one space dimension, a non-local elastic model is based on a single integral law, giving the stress when the strain is known at all spatial points. In this study, we first derive a higher-order Boussinesq equation using locally non-linear theory of 1D non-local elasticity and then we are able to show that under certain conditions the Cauchy problem is globally well-posed.

MSC 2000:: *35Q53 KdV-like equations
74B20 Nonlinear elasticity

Keywords: higher-order Boussinesq equation; non-local elasticity; global well-posedness; Cauchy problem

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Zentralblatt MATH Berlin [Germany]