The Diffusion Equation Involving the Dunkl–Laplacian Operator in a Punctured Domain

Abstract

The purpose of this paper is to establish solvability results for both direct and inverse problems associated with the diffusion equation involving the Dunkl–Laplacian operator in a punctured domain. We demonstrate the existence and uniqueness of solutions for both types of problems. Additionally, explicit formulas for the solutions to the considered problems are derived.

Keywords

• Dunkl operator
• singular Laplacian
• heat equation
• inverse source problem
• direct problem