Inverse Problems of Simultaneous Determination of the Time-Dependent Right-Hand Side Term and the Coefficient in a Parabolic Equation
This work deals with the inverse problem of simultaneous determination of two unknown time-dependent terms in a one-dimensional parabolic equation. The additional information is given by two integral observations. We prove theorems of existence and uniqueness of solution. We also give estimates of maximum modulus of unknown right-hand side and unknown coefficient of the equation with constants derived explicitly in terms of input data.
This work was supported by the Program for improving the competitiveness of universities (NRNU MEPHI).
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