ABSTRACT
In the current paper, we mainly consider the following discrete heat equation on graphs with logarithmic type sources: First, the local existence and uniqueness of the above problem are obtained via the Banach fixed point theorem. By the comparison principle, the quenching behavior of the above problem and the blow-up of its time-derivatives of its solution at finite time under some suitable conditions are also given. Moreover, we also obtain the existence of the critical exponent , when , the above problem admits a global solution by the implicit function theorem. On the other hand, as , its solution will quench at finite time. Finally, a numerical experiment on the graph with five vertexes is used to explain the theoretical results.
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