An Evolutionary Continuous Casting Problem of Two Phases and Its Periodic Behaviour (Journal of Partial Differential Equations, 1989)
The present paper studies a continuous casting problem of two phases: \frac{&#8706H(u)}{&#8706t} + b (t) \frac{&#8706H(u)}{&#8706x} - &#916u = 0 \quad in &#119967&sup1 (&#937_T) where u is che temperature. H (u) is a maximal monotonic graph. &#937_T = G &#215 (0, T), where G = (0, a) &#215 (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.