Analysis uncovers almost global existence of solutions in the BBM equation, suggesting enhanced dynamics.
We study the time of existence of the solutions of the following Benjamin–Bona–Mahony (BBM) equation subject to periodic boundary condition ut − uxxt + ux + uux = 0, u(t,0)=u(t,T), where T stands for the period. We prove an almost global existence result for the above BBM equation by using Birkhoff normal form, which enriched and improved the dynamic properties of BBM equation.
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Mi et al. (2026) studied this question.
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