Quasi-Reversibility Method for an Ill-Posed Nonhomogeneous Parabolic Problem |
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Authors: | Ajoy Jana |
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Institution: | Department of Mathematics, Indian Institute of Technology Madras, Chennai, India |
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Abstract: | The quasi-reversibility method is considered for the non-homogeneous backward Cauchy problem ut+Au = f(t), u(τ) = ? 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∈L1(0,τ],H) and ?∈H. Error analysis is considered when the data ?, f are exact and also when they are noisy. The results obtained generalize and simplify many of the results available in the literature. |
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Keywords: | Ill-posed parabolic problem parameter choice quasi-reversibility method regularization |
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