The multiplicity and asymptotic forms of eigenvalues of vectorial diffusion equations with some certain assumptions

Abstract

The main motivation point of this study is to obtain some novel results on the multiplicity of eigenvalues of diffusion equations. A diffusion equation with some boundary and jump conditions have been analyzed and integral equations have been obtained for the solution under certain initial conditions. Later, integral representations of these solutions have been provided. Finally, asymptotic formulas of eigenvalues with zeros of the characteristic have been considered. A brief conclusion has been given.