Hantaek Bae, Suleyman Ulusoy
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
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 (UNIST), Korea email: hantaek@unist.ac.kr | |
Süleyman Ulusoy Department Of Mathematics and Natural Sciences American University of Ras al Khaimah PO Box 10021,Ras Al Khaimah, UAE email: suleyman.ulusoy@aurak.ac.ae, suleymanulusoy@yahoo.com |
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