Well-posedness for the coupled BBM systems


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 L2-based Sobolev spaces Hs(ℝ) × Hs(ℝ) for s ≥ 0. Under exact conditions on A;… 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.

Publication Title

Journal of Applied Analysis and Computation