The spatial critical points not moving along the heat flow
- Cite this article as:
- Magnanini, R. & Sakaguchi, S. J. Anal. Math. (1997) 71: 237. doi:10.1007/BF02788032
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We consider solutions of the heat equation, in domains inRN, and their spatial critical points. In particular, we show that a solutionu has a spatial critical point not moving along the heat flow if and only ifu satisfies some balance law. Furthermore, in the case of Dirichlet, Neumann, and Robin homogeneous initial-boundary value problems on bounded domains, we prove that if the origin is a spatial critical point never moving for sufficiently many compactly supported initial data satisfying the balance law with respect to the origin, then the domain must be a ball centered at the origin.