WELL-POSEDNESS FOR THE COUPLED BBM SYSTEMS

Hongqiu Chen; Cristina A. Haidau

doi:10.11948/2018.890

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

1 Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA;
2 Department of Computer Science, Northeastern Illinois University, Chicago, IL 60625, USA

Abstract

Abstract

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 H^s(R)×H^s(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.
- Regularized long wave /
- coupled BBM-BBM equations /
- nonlinear dispersive wave equations
MSC: 35Q35;45G15;76B03;35Q51;35Q53;76B15

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References

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