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Blow-up for a semilinear heat equation with Fujita’s critical exponent on locally finite graphs.
- Source :
- Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales / RACSAM; Jul2021, Vol. 115 Issue 3, p1-14, 14p
- Publication Year :
- 2021
-
Abstract
- Let G = (V , E) be a locally finite, connected and weighted graph. We prove that, for a graph satisfying curvature dimension condition C D E ′ (n , 0) and uniform polynomial volume growth of degree m, all non-negative solutions of the equation ∂ t u = Δ u + u 1 + α blow up in a finite time, provided that α = 2 m . We also consider the blow-up problem under certain conditions for volume growth and initial value. These results complement our previous work joined with Lin. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15787303
- Volume :
- 115
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales / RACSAM
- Publication Type :
- Periodical
- Accession number :
- 151340124
- Full Text :
- https://doi.org/10.1007/s13398-021-01075-7