This note is concerned with the singular behaviour of solutions to the heat equation of harmonic maps between Riemannian manifolds. Eells and Sampson Recently, Coron-Ghidaglia [3], Ding [4] and Chen-Ding [2] constructed many examples of finite-time blow-up of the solutions in the case where the domain manifold has dimension greater than two.
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Chang et al. (1992) studied this question.
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