3 papers
math.AP2025
Nonlinear Diffusion Equations on Graphs: Global Well-Posedness, Blow-Up Analysis and Applications
Mengqiu Shao, Yunyan Yang, Liang Zhao
For a nonlinear diffusion equation on graphs whose nonlinearity violates the Lipschitz condition, we prove short-time solution existence and characterize global well-posedness by e…
math.AP2024
Global existence and multiplicity of solutions for logarithmic Schrödinger equations on graphs
Mengqiu Shao
We consider the following logarithmic Schrödinger equation on a locally finite graph , where is a discrete Laplacian operator on the graph,…
math.AP2024
Calculus of variations on hypergraphs
Mengqiu Shao, Yulu Tian, Liang Zhao
We have established a coherent framework for applying variational methods to partial differential equations on hypergraphs, which includes the propositions of calculus and function…