Moser, Roger Weak solutions of a biharmonic map heat flow. (English) Zbl 1165.58008 Adv. Calc. Var. 2, No. 1, 73-92 (2009). 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. Reviewer: Vladimir Balan (Bucureşti) Cited in 9 Documents MSC: 58E20 Harmonic maps, etc. 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) Keywords:biharmonic maps; gradient flow; time discretization; variational problems; weak solutions PDFBibTeX XMLCite \textit{R. Moser}, Adv. Calc. Var. 2, No. 1, 73--92 (2009; Zbl 1165.58008) Full Text: DOI References: [1] Adams D. R., Proc. Amer. Math. Soc. 114 pp 155– (1992) · doi:10.1090/S0002-9939-1992-1076570-5 [2] Chen Y. M., Math. Z. 208 pp 557– (1991) · Zbl 0727.58012 · doi:10.1007/BF02571545 [3] Chen Y. M., Math. Z. 201 pp 83– (1989) · Zbl 0652.58024 · doi:10.1007/BF01161997 [4] Gagliardo E., Ricerche Mat. 8 pp 24– (1959) [5] Gastel A., Adv. Geom. 6 pp 501– (2006) · Zbl 1136.58010 · doi:10.1515/ADVGEOM.2006.031 [6] Haga J., Comput. Vis. Sci. 7 pp 53– (2004) · Zbl 1120.53304 · doi:10.1007/s00791-004-0130-7 [7] Kikuchi N., NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 332 pp 195– [8] DOI: 10.1023/B:AGAG.0000047526.21237.04 · Zbl 1080.58017 · doi:10.1023/B:AGAG.0000047526.21237.04 [9] Calc. Var. Partial Differential Equations 22 pp 421– (2005) · Zbl 1070.58017 · doi:10.1007/s00526-004-0283-8 [10] Moser R., IMRP Int. Math. Res. Pap. 2005 pp 351– (2005) · Zbl 1124.53028 · doi:10.1155/IMRP.2005.351 [11] Nirenberg L., Ann. Scuola Norm. Sup. Pisa 13 pp 115– (3) [12] DOI: 10.1007/BF02567432 · Zbl 0595.58013 · doi:10.1007/BF02567432 [13] J. Differential Geom. 28 pp 485– (1988) [14] Wang C., Math. Z. 247 pp 65– (2004) · Zbl 1064.58016 · doi:10.1007/s00209-003-0620-1 [15] Calc. Var. Partial Differential Equations 21 pp 221– (2004) [16] Comm. Pure Appl. Math. 57 pp 419– (2004) · Zbl 1055.58008 · doi:10.1002/cpa.3045 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.