On the biharmonic heat equation on complete Riemannian manifolds. (English) Zbl 1502.58005
The author studies entire solutions of the biharmonic heat equation on complete Riemannian manifolds without boundary. Uniqueness criteria for the Cauchy problem are derived in this paper. Moreover, the authors derive exponential decay estimates for the biharmonic heat kernel in terms of the Ricci curvature. Result can be viewed as a “maximum principle” for the biharmonic heat equation.
Reviewer: Daniel Ševčovič (Bratislava)
MSC:
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
| 31C12 | Potential theory on Riemannian manifolds and other spaces |
| 35K10 | Second-order parabolic equations |
| 58E20 | Harmonic maps, etc. |
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