In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition $CDE'(n,0)$, the polynomial volume growth of degree $m$, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).
Yiting WU
. BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS[J]. Acta mathematica scientia, Series B, 2024
, 44(2)
: 609
-631
.
DOI: 10.1007/s10473-024-0213-0
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