Nonlocal Problems Arising in Thermoelectrics

Abstract

We revisit the derivation of a nonlocal problem modelling temperature distribution due to power generation using thermoelectric effect. The problem has nonlocal coefficients in reaction and convection terms rather than diffusion term, which makes the problem more interesting. In this paper, we prove that the nonlocal problem has a unique decreasing solution when electric current induced by the thermoelectric effect is small enough.