For u_t = Δu + h(t)u^q on infinite graphs with λ1(G)>0, the paper claims blow-up for fast-growing h and global small data when ∫ h(t)e^{-λ1(q-1)t}dt is finite, but the general blow-up theorem is vitiated by a sign error.
Folz, Gaussian upper bounds for heat kernels of continuous time si mple random walks , Electronic Journal of Probability, 16 (2011), 1693-1755
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On a semilinear parabolic equation with time-dependent source term on infinite graphs
For u_t = Δu + h(t)u^q on infinite graphs with λ1(G)>0, the paper claims blow-up for fast-growing h and global small data when ∫ h(t)e^{-λ1(q-1)t}dt is finite, but the general blow-up theorem is vitiated by a sign error.