Bae, HantaekUlusoy, Suleyman2022-03-312022-03-312017-02-22Bae, H., & Ulusoy, S. (2017). Global well-posedness for nonlinear nonlocal Cauchy problems arising in elasticity. <i>Electronic Journal of Differential Equations, 2017</i>(55), pp. 1-7.1072-6691https://hdl.handle.net/10877/15581In this article, we prove global well-posedness for a family of one dimensional nonlinear nonlocal Cauchy problems arising in elasticity. We consider the equation utt - δLuxx = (β ⁎ [(1 - δ)u + u2n+1])xx, 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.Text7 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear nonlocal wave equationsKernel functionGlobal solutionArticle