Quenching behavior of solutions to heat equations with coupled boundary singularities

摘要

This paper deals with finite time quenching for one-dimensional heat equations coupled via negative singular boundary sources in the more general product form of two component powers u-p1v-q1 and u-p2v-q2. Differently from the generally considered, there are two additional singular factors, namely, u-p1 and v-q2 for the boundary sources of u and v, respectively. We at first propose a criterion to distinguish simultaneous and non-simultaneous quenching, and then determine all possible blow-up rates in the model, three for simultaneous quenching and two for non-simultaneous quenching, under different nominations. This shows real contributions of the two additional singular factors to the quenching behavior of solutions.