刊物主题:Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
出版者:Springer International Publishing
ISSN:1687-2770
文摘
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.
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