Catalytic methane combustion is a highly efficient method for energy conversion at relatively low temperatures and methane concentrations, which simultaneously reduces NO x formation, cuts unburned hydrocarbon and CO emissions, and extends the ignition limits of fuel mixtures [1]. Catalytic methane combustion is used when the stable combustion of a methane-air mixture is impossible or a high degree of methane removal is necessary. From the standpoint of combustion conditions, there can be adiabatic and nonadiabatic catalytic combustion of methane-containing fuel mixtures.In the first method, lean fuel-air mixtures are fed at relatively high temperature to a catalytic monolith and burn under near-adiabatic conditions. This method is typically used in gas turbines [2] and can also be applied to clean gas emissions [3]. In the second method, simultaneously with catalytic combustion, the heat is removed (by convection, conduction, or radiation) from the reaction space, which decreases the catalyst temperature and improves the catalyst operating conditions. This method is mainly used in catalytic furnaces and chemical reactors.The most active components of a methane oxidation catalyst are platinum and/or palladium [1]. In the context of high prices of noble metals, of importance is the problem of saving these metals, which can be solved by creating the optimal distribution of the active component of the catalyst along the catalytic monolith length. Simultaneously, additional problems can be solved, e.g., the creation of a uniform temperature profile along the monolith length for improving the catalyst operating conditions [4] and also the facilitation of the ignition condition of the catalytic monolith [5]. The problem of increasing the efficiency of the catalytic process by creating the optimal distribution of the active component was previously considered for a single catalyst pellet. A theory was developed, a mathematical model was constructed, and the optimal distributions of the active component along the catalytic pellet radius were found for various boundary conditions on the pellet surface [6]. In this case, the problem of optimizing the process in a reactor was formulated as the problem of arranging catalyst pellets with different distributions and concentrations of the active component along the catalyst bed length. For the first time, a mathematical model describing the effect of a nonuniform distribution of the active component along the monolith length in catalytic methane combustion was analyzed by Psyllos and Philippopoulos [7], who, however, did not attempt to find the optimal distribution. For a first-order heterogeneous reaction under isothermal conditions, it was shown that a uniform profile is optimal [8]. In the general case, for an arbitrary kinetic equation, a method for determining the optimal distribution of the active component was presented in our previous work [9]. However, the optimal distributions of the active component under adiabatic conditions were not calculated before.The purpose of...