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On the Rosenau equation. (English) Zbl 0723.35071
Summary: Philip Rosenau introduced the equation $$u_ t+(u+u^ 2)_ x+u_{xxxxt}=0$$, which models approximately the dynamics of certain large discrete systems. We study the Rosenau equation with initial and boundary conditions. To establish global existence and uniqueness, first we show local existence of the mixed problem. Using the fact that the local solution is bounded as an $$H^ 2(\Omega)$$-valued function of t, we establish global existence for the problem.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations
##### Keywords:
Rosenau equation; global existence; uniqueness