Blow-up for the ω-heat equation with Dirichlet boundary conditions and a reaction term on graphs
Qiao Xin, Lü Xu, Chunlai Mu · Applicable Analysis · 2013
In this paper, we consider the blow-up phenomenon for the -heat equation on graph with Dirichlet boundary conditions and a reaction termwhere is called the discrete weighted Laplacian operators. If , every solution is global, and if and under some suitable conditions, we prove that the nonnegative and nontrivial solution blows up in finite time and the blow-up rate on -norm only depends on p. Finally, two examples are proposed to demonstrate our results.