Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222624 | Nonlinear Analysis: Theory, Methods & Applications | 2018 | 12 Pages |
Abstract
Let G=(V,E) be a simple, finite, connected, weighted graph satisfying curvature condition CDEâ²(n,0) and polynomial volume growth V(x,r)â¤c0rm, Îη be the normalized Laplacian. In this paper we prove that the semilinear heat equation ut=Îηu+u1+α on G has no non-negative global solutions for any bounded, non-negative and non-trivial initial value in the case of mα=2. The obtained result provides a significant complement to the work that was done recently by Lin and Wu (2017) concerning the existence and nonexistence of global solutions for the semilinear heat equation on graphs.
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Authors
Yiting Wu,