Incomplete quenching of heat equations with coupled singular logarithms boundary fluxes

Abstract This paper deals with quenching phenomena for a heat equations with coupled singular logarithms boundary fluxes. Under appropriate hypotheses, the non-simultaneous quenching of the solution for the system is proved, and the estimates of quenching rates are given. Then we give a natural continuation of the solution ( u , v ) after the quenching time when the equations occurs non-simultaneous quenching. Moreover, we identify the heat equations verified by the continuation beyond quenching time, i.e., the equations occurs incomplete quenching.

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