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Weak solutions of a biharmonic map heat flow. (English) Zbl 1165.58008

One of the several fourth order analogues of the harmonic map heat flow is studied. It is shown that for an open bounded domain \(\Omega\subset{\mathbb R}^n\) (\(4\leq n\leq8\)) and a compact, smooth Riemannian manifold \(N\) isometrically embedded into \({\mathbb R}^n\) – as codomain, the problem permits the construction of weak solutions with a time discretization method.

MSC:

58E20 Harmonic maps, etc.
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
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