A Higher-order Boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity
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CitationDuruk, N., Erkip, A. & Erbay, H. A. (2009). A higher-order boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 74(1), 97-106. doi:10.1093/imamat/hxn020
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.