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Asymptotic behaviour for \(t\to+\infty\) of the solution of the Riquier problem. (Russian) Zbl 0825.35015

The temporal behaviour for \(t\to+\infty\) of the solution of the Riquier problem is studied for the equation \(U_ t=(-1)^{\nu-1}\Delta^ \nu U\) in the exterior of the sufficiently smooth and closed contour \(\Gamma\) with a positive curvature. It is proved that the solution of the problem behaves for \(t\to+\infty\) as the solution of the corresponding Cauchy problem.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35K35 Initial-boundary value problems for higher-order parabolic equations
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