Heat Kernel Estimate in a Conical Singular Space

Heat Kernel Estimate for ∆+∆ in C open sets

We consider a family of pseudo differential operators {∆ + a∆; a ∈ (0, 1]} on R for every d ≥ 1 that evolves continuously from ∆ to ∆ + ∆, where α ∈ (0, 2). It gives rise to a family of Lévy processes {X, a ∈ (0, 1]} in R, where X is the sum of a Brownian motion and an independent symmetric α-stable process with weight a. We establish sharp two-sided estimates for the heat kernel of ∆ + a∆ with...

Heat Kernel Estimate for ∆ + ∆α/2 in C1,1 open sets

We consider a family of pseudo differential operators {∆ + a∆; a ∈ (0, 1]} on R for every d ≥ 1 that evolves continuously from ∆ to ∆ + ∆, where α ∈ (0, 2). It gives rise to a family of Lévy processes {Xa, a ∈ (0, 1]} in R, where X is the sum of a Brownian motion and an independent symmetric α-stable process with weight a. We establish sharp two-sided estimates for the heat kernel of ∆ + a∆ wit...

Reproducing Kernel Hilbert Space(RKHS) method for solving singular perturbed initial value problem

In this paper, a numerical scheme for solving singular initial/boundary value problems presented.By applying the reproducing kernel Hilbert space method (RKHSM) for solving these problems,this method obtained to approximated solution. Numerical examples are given to demonstrate theaccuracy of the present method. The result obtained by the method and the exact solution are foundto be in good agr...

Solving a Volterra integral equation with weakly singular kernel in the reproducing kernel space

Abstract In this paper, we will present a new method for a Volterra integral equation with weakly singular kernel in the reproducing kernel space. Firstly the equation is transformed into a new equivalent equation. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation un(t) to the exact solution u(t) is obtained. Some...

An Estimate on the Heat Kernel ofMagnetic Schr