2018 Volume 8 Issue 3
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Hongqiu Chen, Cristina A. Haidau. WELL-POSEDNESS FOR THE COUPLED BBM SYSTEMS[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 890-914. doi: 10.11948/2018.890
Citation: Hongqiu Chen, Cristina A. Haidau. WELL-POSEDNESS FOR THE COUPLED BBM SYSTEMS[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 890-914. doi: 10.11948/2018.890

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.
    MSC: 35Q35;45G15;76B03;35Q51;35Q53;76B15
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