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A higher-order Boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity. (English) Zbl 1156.35458
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:
35Q53KdV-like (Korteweg-de Vries) equations
74B20Nonlinear elasticity