Quenching behavior of solutions in coupled heat equations with singular multi-nonlinearities

In this paper we study the quenching behavior of solutions to coupled heat equations with singular multi-nonlinearities. We at first identify simultaneous and non-simultaneous quenching, and then establish four kinds of simultaneous quenching rates, which are uniformly represented via the characteristic algebraic system introduced for the model. A precise classification of parameters is given for the multiple simultaneous quenching rates. For example, we distinguish between two kinds of subcases, with or without particular requirements on initial data, realizing a common simultaneous quenching rate. On the other hand, it is interesting to find that there are two simultaneous quenching rates which share a common subregion of parameters, determined by the initial data assumed.