### ON AN ESTIMATE FOR THE MODULUS OF CONTINUITY OF A NONLINEAR INVERSE PROBLEM

#### Abstract

A reverse time problem is considered for a semilinear parabolic equation. Two-sided estimates are obtained for the norms of values of a nonlinear operator in terms of the norms of values of the corresponding linear operator. As a consequence, two-sided estimates are established for the modulus of continuity of a semilinear inverse problem in terms of the modulus of continuity of the corresponding linear problem.

#### Keywords

Parabolic equation; Inverse problem; Modulus of continuity of the inverse operator; Approximate method; Error estimate

#### Full Text:

PDF#### References

- Vasin V.V., Ageev A.L. Inverse and Ill-posed problems with a priori information. Inverse and Ill-Posed Problems Series. Utrecht: VSP, 1995. 255p.
- Ivanov V.K., Vasin V.V., Tanana V.P. Theory of linear ill-posed problems and its applications. Inverse and Ill-Posed Problems Series. Walter de Gruyter, 2002. 294 p.
- Ivanov V.K., Korolyuk T.I. Error estimates for solutions of incorrectly posed linear problems // USSR Computational Mathematics and Mathematical Physics. 1969. Vol. 9, no. 1. P. 35–49.
- Mikhlin S.G. Mathematical physics; an advanced course. Amsterdam, Norhth-Holland Pub.Co., 1970. 562p.
- Bakushinsky A.B., Kokurin M.Yu. Iterative methods for approximate solution of inverse problems. Mathematics and its Applications. Vol. 577. Dordrecht: Springer, 2004. 291 p.
- Strakhov V.N. On solving linear ill-posed problems in a Hilbert space // Diff. equations. 1970. Vol. 6, iss. 8. P. 1990–1995.
- Tabarintseva E.V. On error estimation for the quasi-inversion method for solving a semi-linear ill-posed problem // Sib. Zh. Vychisl. Mat. 2005. Vol. 8, iss. 3. P. 259–271.
- Tanana V.P., Tabarintseva E.V. On a method to approximate discontinuous solutions of nonlinear inverse problems // Sib. Zh. Vychisl. Mat. 2007. Vol. 10, iss. 2. P. 221–228.
- Tanana V.P. On the convergence of regularized solutions of nonlinear operator equations // Sib. Zh. Ind. Mat. 2003. Vol. 6, iss. 3. P. 119–133.
- Tanana V.P. Optimal order methods of solving non-linear ill-posed problems // USSR Computational Mathematics and Mathematical Physics. 1976. Vol. 16, iss. 2. P. 219–225.
- Tikhonov A.N., Leonov A.S., Yagola A.G. Nonlinear ill-posed problems. Chapman & Hall, 1998. 387p.

#### Article Metrics

Metrics Loading ...

### Refbacks

- There are currently no refbacks.