Quasi-Reversibility Method for an Ill-Posed Nonhomogeneous Parabolic Problem. (1st December 2016) - Jana, Ajoy; Nair, M. Thamban
ABSTRACT: The quasi-reversibility method is considered for the non-homogeneous backward Cauchy problem u t + Au  =  f ( t ), u ( τ ) =  ϕ for 0≤ t < τ, which is known to be an ill-posed problem. Here, A is a densely defined positive self-adjoint unbounded operator on a Hilbert space H with given data f ∈ L 1 ([0, τ ], H ) and ϕ ∈ H . Error analysis is considered when the data ϕ, f are exact and also when they are noisy. The results obtained generalize and simplify many of the results available in the literature.