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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.12303 |
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Table of Contents:
- In this paper, we study blow up behavior of the semilinear parabolic inequality with $p$-Laplacian operator and nonlinear source $u_t - Δ_p u \geq σ(x, t)Φ(u)$ on a locally finite connected weighted graph $G = (V, E)$. We extend the comparison principle and thereby establish the relationship between the initial value and the existence of blow-up solutions to the problem under different growth rates of $Φ$. We prove that when the growth rate of $Φ$ exceeds linear growth, blow-up solutions exist under appropriate initial conditions.