Quenching of the solution to the discrete heat equation with logarithmic type sources on graphs

In the current paper, we mainly consider the following discrete heat equation on graphs with logarithmic type sources: ut=Δρu+λln⁡u,x∈S, t∈(0,Tmax),u(x,t)=1,x∈∂S, t∈(0,Tmax),u(x,0)=u0(x),x∈S. 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...