Анализ данных Коши в некорректных задачах продолжения решения с части границы

Анализ данных Коши в некорректных задачах продолжения решения с части границы

Кабанихин С. И., Шишленин М. А.

УДК 519.63,519.64 
DOI: 10.33048/semi.2025.22.A16  
MSC 65N21,65R32


Аннотация:

The paper analyzes the ill-posedness of the Cauchy problem with data on a part of the boundary for partial differential equations. The variants of the boundaries of the region (time-like, characteristic, space-like) are considered, in which the Cauchy data on the part of the boundary are interconnected. The conditions are obtained, the violation of which leads to instability of the continuation problem.

Ключевые слова: ill-posed problem, continuation problems, Cauchy problem, Laplace equation, Helmholtz equation, wave equation, Dirichlet and Neumann data