Partial differential equations (PDEs) involving fractional Laplace operators have been increasingly used to model non-local diffusion processes and are actively investigated using both analytical numerical approaches. The purpose of this work is study the effects spectral Laplacian on bifurcation structure reaction-diffusion systems bounded domains. In order do we use advanced continuation tech...

In the first part of this paper, we study the heat equation and the heat kernel associated with the Heckman-Opdam Laplacian in the compact, Weyl-group invariant setting. In particular, this Laplacian gives rise to a Feller-Markov semigroup on a fundamental alcove of the affine Weyl group. The second part of the paper is devoted to the Segal-Bargmann transform in our context. A Hilbert space of ...

This paper proposed a robust searching algorithm to generate path planning for mobile robot. The searching algorithm employs Laplacian Behaviour-Based Control (LBBC) during space exploration of the environment. The LBBC make use of the potential function in the configuration space to guide its exploration. Laplace’s equation was used to represent the potential function in the configuration spac...

We study the game theoretic p-Laplacian for semi-supervised learning on graphs, and show that it is well-posed in the limit of finite labeled data and infinite unlabeled data. In particular, we show that the continuum limit of graph-based semi-supervised learning with the game theoretic p-Laplacian is a weighted version of the continuous p-Laplace equation. Our proof uses the viscosity solution...