Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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APPLICATION OF ROTHE'S METHOD TO A NONLINEAR WAVE EQUATION ON GRAPHS

  • Lin, Yong (Yau Mathematical Sciences Center Tsinghua University) ;
  • Xie, Yuanyuan (Department of Mathematics Tianjin University of Finance and Economics, School of Mathematics Renmin University of China)
  • Received : 2021.06.08
  • Accepted : 2021.11.03
  • Published : 2022.05.31
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Abstract

We study a nonlinear wave equation on finite connected weighted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption. For linear wave equation on graphs, Lin and Xie [10] obtained the existence and uniqueness of solution. The main novelty of this paper is that the wave equation we considered has the nonlinear damping term |ut|p-1·ut (p > 1).

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Acknowledgement

This work is supported by the National Science Foundation of China [12071245].

References

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