Global well-posedness for nonlinear nonlocal Cauchy problems arising in elasticity
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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
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.
CitationBae, H., & Ulusoy, S. (2017). Global well-posedness for nonlinear nonlocal Cauchy problems arising in elasticity. Electronic Journal of Differential Equations, 2017(55), pp. 1-7.
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