On the Heat Flow for Harmonic Maps with Potential |
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Authors: | Ali Fardoun Andrea Ratto Rachid Regbaoui |
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Institution: | (1) Département de Mathématiques, Université de Brest, 6, Avenue Le Gorgeu, 29285 Brest, France. e-mail;(2) Dipartimento di Matematica, Facoltà di Ingegneria, Viale Merello 93, 09123 Cagliari, Italy;(3) Département de Mathématiques, Université de Brest, 6, Avenue Le Gorgeu, 29285 Brest, France |
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Abstract: | Let (M, g) and (N, h) be twoconnected Riemannian manifolds without boundary (M compact,N complete). Let G C
(N): ifu: M N is a smooth map, we consider the functional E
G
(u) = (1/2)
M
|du|2– 2G(u)]dV
M
and we study its associated heat equation. Inthe compact case, we recover a version of the Eells–Sampson theorem,while for noncompact target manifold N, we establishsuitable hypotheses and ensure global existence and convergence atinfinity. In the second part of the paper, we study phenomena of blowingup solutions. |
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Keywords: | harmonic maps heat equation |
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