A simple regularization method for the ill-posed evolution equation

Nguyen Huy Tuan; Dang Duc Trong

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 1, page 85-95
  • ISSN: 0011-4642

Abstract

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The nonhomogeneous backward Cauchy problem u t + A u ( t ) = f ( t ) , u ( T ) = ϕ , 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.

How to cite

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Tuan, Nguyen Huy, and Trong, Dang Duc. "A simple regularization method for the ill-posed evolution equation." Czechoslovak Mathematical Journal 61.1 (2011): 85-95. <http://eudml.org/doc/196363>.

@article{Tuan2011,
abstract = {The nonhomogeneous backward Cauchy problem \[u\_t +Au(t) = f(t),\quad u(T) = \varphi \] , 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.},
author = {Tuan, Nguyen Huy, Trong, Dang Duc},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear parabolic problem; backward problem; semigroup of operators; ill-posed problem; contraction principle; nonlinear parabolic problem; backward problem; semigroup of operators; ill-posed problem; contraction principle},
language = {eng},
number = {1},
pages = {85-95},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A simple regularization method for the ill-posed evolution equation},
url = {http://eudml.org/doc/196363},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Tuan, Nguyen Huy
AU - Trong, Dang Duc
TI - A simple regularization method for the ill-posed evolution equation
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 85
EP - 95
AB - The nonhomogeneous backward Cauchy problem \[u_t +Au(t) = f(t),\quad u(T) = \varphi \] , 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.
LA - eng
KW - nonlinear parabolic problem; backward problem; semigroup of operators; ill-posed problem; contraction principle; nonlinear parabolic problem; backward problem; semigroup of operators; ill-posed problem; contraction principle
UR - http://eudml.org/doc/196363
ER -

References

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