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The Backscattering Problem for Time-Dependent Potentials.

Medet Nursultanov1,2, Lauri Oksanen1, Plamen Stefanov3

  • 1Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland.

Annales Henri Poincare
|June 15, 2026
PubMed
Summary
This summary is machine-generated.

This study addresses the inverse backscattering problem for time-dependent potentials. Researchers proved uniqueness and Lipschitz stability for recovering small potentials.

Keywords:
35R3047F05Primary 35P25Secondary 35L05

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Area of Science:

  • Mathematical Physics
  • Inverse Problems

Background:

  • The inverse backscattering problem aims to determine potential functions from scattered wave data.
  • Time-dependent potentials introduce complexities compared to static potentials.

Purpose of the Study:

  • To investigate the inverse backscattering problem for time-dependent potentials.
  • To establish theoretical guarantees for potential recovery.

Main Methods:

  • Utilizing techniques from partial differential equations.
  • Applying stability analysis to inverse scattering theory.

Main Results:

  • Demonstrated uniqueness of solution for the inverse problem.
  • Proved Lipschitz stability for the reconstruction of small potentials.

Conclusions:

  • The findings provide a foundation for analyzing time-dependent inverse scattering problems.
  • Guarantees of uniqueness and stability are crucial for practical applications in potential recovery.