Global solutions of semilinear parabolic equations on negatively curved Riemannian manifolds. (English) Zbl 1461.35130
Summary: We are concerned with global existence for semilinear parabolic equations on Riemannian manifolds with negative sectional curvatures. A particular attention is paid to the class of initial conditions which ensure existence of global solutions. Indeed, we show that such a class is crucially related to the curvature bounds. A crucial point in our arguments is the construction of positive bounded supersolutions to the eigenvalue equation.
MSC:
| 35K58 | Semilinear parabolic equations |
| 35B51 | Comparison principles in context of PDEs |
| 35B44 | Blow-up in context of PDEs |
| 35K08 | Heat kernel |
| 35R01 | PDEs on manifolds |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
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