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On the Rosenau equation in multidimensional space. (English) Zbl 0811.35142
The author generalizes some results he obtained (in his Phd thesis) on the Rosenau equation \[ u_ t + u_{xxxxt} = \varphi (u)_ x, \quad x \in \Omega, \quad t \in (0, \infty), \quad u(0,x) = u_ 0(x), \quad x \in \Omega \] with Dirichlet boundary conditions. He considers a mixed problem with Dirichlet boundary conditions, and he derives global existence of solutions.

MSC:
35Q58 Other completely integrable PDE (MSC2000)
35K35 Initial-boundary value problems for higher-order parabolic equations
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[1] Rosenau, Ph., Dynamics of dense discrete systems, Prog. theoret. phys, 79, 1028-1042, (1988)
[2] Park, M.A., Model equations in fluid dynamics, ()
[3] Adams, R.A., Sobolev spaces, (1975), Academic Press New York · Zbl 0186.19101
[4] Goldstein, J.A., Semigroups of linear operators and applications, (1985), Oxford University Press New York · Zbl 0592.47034
[5] Goldstein J.A., Kajikiya R. & Oharu S., On some nonlinear dispersive equations in several space variables, Diff. Integral Eqns (to appear). · Zbl 0735.35103
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