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Hadron-quark combustion in dense matter is a central topic in the study of phases in compact stars and their high-energy astrophysics. We critically reviewed the literature on hadron-quark combustion, dividing them into a "first wave" that treats the problem as a steady-state burning with or without constraints of mechanical equilibrium, and a "second wave" which uses numerical techniques to resolve the burning front and solves the underlying partial differential equations for the chemistry ofdoi:10.3390/universe5060136 fatcat:bx4nscb3xnaq5crteqajgfn3be