Publication Date:
2015-12-04
Description:
We consider the periodic initial value problem associated to the generalized Benjamin-Bona-Mahony equation with generalized damping on the one dimensional torus. In contrast to the classical BBM equation, the main difference is that the generalized equation contains two nonlocal operators, and the main difficulty comes from two nonlocal operators. By the fixed point theorem, we prove that the periodic initial value problem is locally well-posed. We also prove that if the solution exists globally in time, it exhibits some asymptotic behavior.MSC: 35A07, 35Q53.
Print ISSN:
1687-2762
Electronic ISSN:
1687-2770
Topics:
Mathematics
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