2023
DOI: 10.1051/m2an/2023006
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Continuum limit of [[EQUATION]]-Laplacian evolution problems on graphs: [[EQUATION]]graphons and sparse graphs

Abstract: In this paper we study continuum limits of the discretized [[EQUATION]] -Laplacian evolution problem on sparse graphs with homogeneous Neumann boundary conditions. This goes far beyond known results by handling much more general class of kernels, possibly singular, and graph sequences whose limit are the so-called [[EQUATION]] -graphons. More precisely, we derive a bound on the distance between two continuous-in-time trajectories defined by two different evolution systems (i.e. with different kernels, second m… Show more

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