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Regularization of backward parabolic equations in Banach spaces
-
Dinh Nho Hào
und
Nguyen Van Duc
Veröffentlicht/Copyright:
14. Dezember 2012
Abstract.
The ill-posed backward parabolic equation
with a densely defined linear operator A such that 
generates an analytic semigroup 
in a Banach space X and 
being given
is stabilized by the Tikhonov
regularization method and by the well-posed non-local boundary value
problem
A priori and a posteriori parameter choice rules for these
regularization methods are suggested which yield the error estimate
for all 
, where 
are computable constants, E
is a bound for 
and 
is a defined harmonic function.
Keywords: Backward parabolic equations; ill-posed problems; Tikhonov regularization; non-local boundary value
problems
Received: 2012-06-19
Published Online: 2012-12-14
Published in Print: 2012-12-01
© 2012 by Walter de Gruyter Berlin Boston
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- Masthead
- Extra-optimal methods for solving ill-posed problems
- Regularization for ill-posed parabolic evolution problems
- Satisfier function in Ritz–Galerkin method for the identification of a time-dependent diffusivity
- On some identification problem for source function to one semievolutionary system
- Regularization of backward parabolic equations in Banach spaces
- On the existence of global saturation for spectral regularization methods with optimal qualification
- Inverse determination of unsteady temperatures and heat fluxes on inaccessible boundaries
- Well-posedness of the Cauchy problem to a nonlinear magnetoelastic system in 1-D periodic media
- A family of rules for the choice of the regularization parameter in the Lavrentiev method in the case of rough estimate of the noise level of the data
- Inverse problems for second-order differential pencils with Dirichlet boundary conditions
Schlagwörter für diesen Artikel
Backward parabolic equations;
ill-posed problems;
Tikhonov regularization;
non-local boundary value
problems
Artikel in diesem Heft
- Masthead
- Extra-optimal methods for solving ill-posed problems
- Regularization for ill-posed parabolic evolution problems
- Satisfier function in Ritz–Galerkin method for the identification of a time-dependent diffusivity
- On some identification problem for source function to one semievolutionary system
- Regularization of backward parabolic equations in Banach spaces
- On the existence of global saturation for spectral regularization methods with optimal qualification
- Inverse determination of unsteady temperatures and heat fluxes on inaccessible boundaries
- Well-posedness of the Cauchy problem to a nonlinear magnetoelastic system in 1-D periodic media
- A family of rules for the choice of the regularization parameter in the Lavrentiev method in the case of rough estimate of the noise level of the data
- Inverse problems for second-order differential pencils with Dirichlet boundary conditions
