A mixed problem is considered for a system of partial differential equations modeling the process of adsorption dynamics. An existence and uniqueness theorem is proved for this problem, and the solution properties are investigated. The inverse problem is posed, involving the determination of the system coefficient given additional information about the solution. A uniqueness theorem is proved for the solution of the inverse problem.We consider the inverse problem for a model of adsorption dynamics. Inverse problems of adsorption dynamics have been studied by many authors (see, e.g., [1 -4]).Consider the following mathematical model of adsorption dynamics:Hereλ are positive constants, λ > β. The functions µ(t) and F (x) satisfy the following conditions: µ ∈ C[0, T ], µ(0) = 0,