The Multiplicity of Eigenvalues of a Vectorial Diffusion Equations with Discontinuous Function Inside A Finite Interval

Abstract

In this study, diffusion operator with discontinuity function is considered. Integral equations have been obtained for the solution under certain initial conditions. Furthermore, we obtained integral representations for these solutions. Some equations have been obtained by the kernel functions. By using the characteristic function, asymptotic formulas of eigenvalues with zeros of the characteristic are obtained. In this study, diffusion operator with discontinuity function is considered. Integral equations have been obtained for the solution under certain initial conditions. Furthermore, we obtained integral representations for these solutions. Some equations have been obtained by the kernel functions. By using the characteristic function, asymptotic formulas of eigenvalues with zeros of the characteristic are obtained.