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We consider a Cahn–Hilliard equation in a bounded domain Ω inℝ  n{\mathbb{R}^{n}}    over a time interval(  0  ,  T  ){(0,T)}    and discuss the backward problem in time of determining intermediate datau  ⁢   (  x  ,  θ  ){u(x,\theta)}   ,θ  ∈   (  0  ,  T  ){\theta\in(0,T)}   ,x  ∈  Ω{x\in\Omega}    from the measurement of the final datau  ⁢   (  x  ,  T  ){u(x,T)}   ,x  ∈  Ω{x\in\Omega}   . Under suitable a priori boundness assumptions on the solutionsu  ⁢   (  x  ,  t  ){u(x,t)}   , we prove a conditional stability estimate for the semilinear Cahn–Hilliard equation

Conditional stability in a backward Cahn–Hilliard equation via a Carleman estimate