Blow-up problems for nonlinear parabolic equations on locally finite graphs

Yong Lin Department of Mathematics, Renmin University of China, Beijing 100872, China Yiting Wu Department of Mathematics, Renmin University of China, Beijing 100872, China

Analysis of PDEs mathscidoc:2207.03006

Acta Mathematica Scientia, 38, (3), 843-856, 2018.5
Let G=(V,E) be a locally finite connected weighted graph, and Δ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation u_t = Δu + f(u) on G. The blow-up phenomenons for u_t = Δu + f(u) are discussed in terms of two cases: (i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.
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@inproceedings{yong2018blow-up,
  title={Blow-up problems for nonlinear parabolic equations on locally finite graphs},
  author={Yong Lin, and Yiting Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707152640100269563},
  booktitle={Acta Mathematica Scientia},
  volume={38},
  number={3},
  pages={843-856},
  year={2018},
}
Yong Lin, and Yiting Wu. Blow-up problems for nonlinear parabolic equations on locally finite graphs. 2018. Vol. 38. In Acta Mathematica Scientia. pp.843-856. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707152640100269563.
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