Mengqiu Shao

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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 SchrÃ¶dinger equations on graphs

Mengqiu Shao

We consider the following logarithmic SchrÃ¶dinger equation $- I^ u + h (x) u = u lo g u^{2}$ on a locally finite graph $G = (V, E)$ , where $I^$ is a discrete Laplacian operator on the gra…

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…