An Evolutionary Continuous Casting Problem of Two Phases and Its Periodic Behaviour

Abstract

The present paper studies a continuous casting problem of two phases: \frac{∂H(u)}{∂t} + b (t) \frac{∂H(u)}{∂x} - Δu = 0 \quad in 𝒟¹ (Ω_T) where u is che temperature. H (u) is a maximal monotonic graph. Ω_T = G × (0, T), where G = (0, a) × (0. 1) stands for the ingot. We obtain the existence and the uniqueness of weak solution and the existence of periodic solution for the first boundary problem.