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Porous media equation on locally finite graphs

Li Ma — 2022

Archivum Mathematicum

In this paper, we consider two typical problems on a locally finite connected graph. The first one is to study the Bochner formula for the Laplacian operator on a locally finite connected graph. The other one is to obtain global nontrivial nonnegative solution to porous-media equation via the use of Aronson-Benilan argument. We use the curvature dimension condition to give a characterization two point graph. We also give a porous-media equation criterion about stochastic completeness of the graph....

Exponential H filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays

Li MaMeimei XuRuting JiaHui Ye — 2014

Kybernetika

This paper is concerned with the exponential H filter design problem for stochastic Markovian jump systems with time-varying delays, where the time-varying delays include not only discrete delays but also distributed delays. First of all, by choosing a modified Lyapunov-Krasovskii functional and employing the property of conditional mathematical expectation, a novel delay-dependent approach is developed to deal with the mean-square exponential stability problem and H control problem. Then, a mean-square...

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