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In this paper we discuss existence for a mathematical model of the enzyme reaction process described by a reaction-diffusion equation under initial and boundary conditions. Some existence conditions which guarantee solvability are considered. A unique exponentially asymptotically stable solution of the considered problem is shown. Uniqueness and ununiqueness are discussed as well. AMS Subject Classification: 35K20, 35B35, 35K57

ON THE EXISTENCE FOR AN ENZYME REACTION MODEL