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A simple regularization method for the ill-posed evolution equation

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Abstract

The nonhomogeneous backward Cauchy problem

$$ u_t + Au(t) = f(t),u(T) = \phi $$

where A is a positive self-adjoint unbounded operator which has continuous spectrum and f is a given function being given is regularized by the well-posed problem. New error estimates of the regularized solution are obtained. This work extends earlier results by N. Boussetila and by M. Denche and S. Djezzar.

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Authors and Affiliations

  1. Ho Chi Minh City, Viet Nam

    Nguyen Huy Tuan & Dang Duc Trong

  2. Department of Mathematics, Saigon University, 273 An Duong Vuong, District 5, Ho Chi Minh City, Viet Nam

    Nguyen Huy Tuan

  3. Department of Mathematics, Ho Chi Minh City National University, 227 Nguyen Van Cu, Q. 5, Ho Chi Minh City, Viet Nam

    Dang Duc Trong

Authors
  1. Nguyen Huy Tuan
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  2. Dang Duc Trong
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Correspondence to Nguyen Huy Tuan.

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Tuan, N.H., Trong, D.D. A simple regularization method for the ill-posed evolution equation. Czech Math J 61, 85–95 (2011). https://doi.org/10.1007/s10587-011-0019-9

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  • DOI: https://doi.org/10.1007/s10587-011-0019-9

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