ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, v.2017, no.55, pp.1 - 7
Abstract
In this article, we prove global well-posedness for a family of one dimensional nonlinear nonlocal Cauchy problems arising in elasticity. We consider the equation (Formula present) where L is a differential operator, β is an integral operator, and δ = 0 or 1. (Here, the case δ = 1 represents the additional doubly dispersive effect.) We prove the global well-posedness of the equation in energy spaces.