Analysis of non-classical heat conduction models

Abstract

Let 𝑡 > 0 be the time variable, х – the spatial variable where 0 ≤ 𝑥 ≤ 𝑙 and 𝑓, 𝜑, 𝜇1, 𝜇2 be known function of their arguments. Let 𝑢(𝑥, 𝑡) be unknown function representing temperature of a rod positioned along the Ox axis, where 0 ≤ 𝑥 ≤ 𝑙.