1. On nonexistence of global solutions for a semilinear heat equation on graphs.
- Author
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Wu, Yiting
- Subjects
- *
NUMERICAL solutions to heat equation , *EXISTENCE theorems , *GLOBAL analysis (Mathematics) , *GRAPH theory , *CURVATURE , *POLYNOMIALS - Abstract
Let G = ( V , E ) be a simple, finite, connected, weighted graph satisfying curvature condition C D E ′ ( n , 0 ) and polynomial volume growth V ( x , r ) ≤ c 0 r m , Δ η be the normalized Laplacian. In this paper we prove that the semilinear heat equation u t = Δ η u + u 1 + α on G has no non-negative global solutions for any bounded, non-negative and non-trivial initial value in the case of m α = 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. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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