Semilinear heat equations and parabolic variational inequalities on graphs

Yong Lin Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China Yuanyuan Xie School of Mathematics, Renmin University of China, Beijing, 100872, China

Analysis of PDEs mathscidoc:2207.03010

arXiv, 2021.8
Let G=(V,E) be a locally finite connected weighted graph, and Ω be an unbounded subset of V. Using Rothe's method, we study the existence of solutions for the semilinear heat equation ∂_t u+|u|^{p−1}⋅u=Δu (p≥1) and the parabolic variational inequality ∫_{Ω^∘} ∂_t u⋅(v−u)dμ ≥ ∫_{Ω^∘} (Δu+f)⋅(v−u)dμ for any v∈H, where H={u∈W^{1,2}(V):u=0 on V∖Ω^∘}.
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@inproceedings{yong2021semilinear,
  title={Semilinear heat equations and parabolic variational inequalities on graphs},
  author={Yong Lin, and Yuanyuan Xie},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707160802109025579},
  booktitle={arXiv},
  year={2021},
}
Yong Lin, and Yuanyuan Xie. Semilinear heat equations and parabolic variational inequalities on graphs. 2021. In arXiv. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707160802109025579.
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