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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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| _version_ | 1866915442170265600 |
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| author | Ma, Wenyuan Zhao, Liang |
| author_facet | Ma, Wenyuan Zhao, Liang |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blow-up solutions of parabolic $p$-Laplacian inequalities on locally finite graphs Ma, Wenyuan Zhao, Liang Analysis of PDEs 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. |
| title | Blow-up solutions of parabolic $p$-Laplacian inequalities on locally finite graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.12303 |