Hantaek Bae, Suleyman Ulusoy
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
where is a differential operator, is an integral operator, and or 1. (Here, the case represents the additional doubly dispersive effect.) We prove the global well-posedness of the equation in energy spaces.
Submitted May 24, 2016. Published February 22, 2017.
Math Subject Classifications: 35Q74, 35L15, 74B20.
Key Words: Nonlinear nonlocal wave equations; kernel function; global solution.
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| Hantaek Bae |
Department of Mathematical Sciences
Ulsan National Institute of Science and Technology
| Süleyman Ulusoy |
Department Of Mathematics and Natural Sciences
American University of Ras al Khaimah
PO Box 10021,Ras Al Khaimah, UAE
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