A nonlinearly backward heat problem: uniqueness, regularization and error estimate

Abstract

We consider the problem of finding, from the final data u(x,T) = ϕ(x), the temperature u satisfying

The problem is nonlinearly ill-posed. We shall use the Fourier transforms to get a nonlinear integral equation and give a regularized solution by perturbing directly the integral equation. Error estimates are given.

Keywords:

• Backward heat problem
• Contraction principle
• Nonlinearly ill-posed problem

Keywords:

• Mathematics Subject Classification 2000: 35K05
• 35K99
• 47J06
• 47H10

Acknowledgment

Supported by the Council for Natural Science of Vietnam.