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Volume 8, Number 3, 2018, Pages 890-914                                                                DOI:10.11948/2018.890
Well-posedness for the coupled BBM systems
Hongqiu Chen and Cristina A. Haidau
Keywords:Regularized long wave, coupled BBM-BBM equations, nonlinear dispersive wave equations.
      Consideration is given to initial value problem for systems of two evolution equations of generalized BBM-type coupled through nonlinearity described in (1.3). It is shown that the problem is always locally well-posed in the $L_2$-based Sobolev spaces $H^s(\mathbb{R}) \times H^s(\mathbb{R})$ for $s \ge 0$. Under exact conditions on $A, \cdots, F,$ the local well-posedness theory extends globally, and bounds for the growth in time of relevant norms of solutions corresponding to very general auxiliary data are derived.
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