In this work we study the degenerate diffusion equation ∂t=xαa(x)∂x2+b(x)∂x for (x,t)∈(0,∞)2, equipped with a Cauchy initial data and Dirichlet boundary condition at 0. We assume that order of degeneracy 0 operator is α∈(0,2), coefficient functions (and their derivatives) are only locally bounded. adopt combination probabilistic approach analytic method: by analyzing behaviors underlying proces...

In this work, the localized method of fundamental solution (LMFS) is extended to Signorini problem. Unlike traditional (MFS), LMFS approximates field quantity at each node by using quantities adjacent nodes. The idea similar domain type method. fictitious boundary nodes are proposed impose condition and governing equations formulate a sparse matrix. inequality problem solved indirectly introduc...