Abstract
Let \(G=(V,E)\) be a locally finite, connected and weighted graph. We prove that, for a graph satisfying curvature dimension condition \(CDE'(n,0)\) and uniform polynomial volume growth of degree m, all non-negative solutions of the equation \(\partial _tu=\Delta u+u^{1+\alpha }\) blow up in a finite time, provided that \(\alpha =\frac{2}{m}\). 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have