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This paper is concerned with identification of a spatial source function fromfinal time observation in a bi-parabolic equation, where the full sourcefunction is assumed to be a product of time dependent and a space dependentfunction. Due to the ill-posedness of the problem, recently some authors haveemployed different regularization method and analysed the convergence rates.But, to the best of our knowledge, the quasi-reversibility method is notexplored yet, and thus we study that in this paper. As an importantimplication, the H{\"o}lder rates for the apriori and aposteriori errorestimates obtained in this paper improve upon the rates obtained in earlierworks. Also, in some cases we show that the rates obtained are of optimalorder. Further, this work seems to be the first one that has broaden theapplicability of the problem by allowing the time dependent component of thesource function to change sign. To the best of our knowledge, the earlier knownwork assumed the fixed sign of the time dependent component by assuming somebounded below condition.

A source identification problem in a bi-parabolic equation: convergence rates and some optimal results