The paper considers the question of the possibility of recovering symmetric stable states of a bistable medium in the inverse problem for a nonlinear singularly perturbed autowave equation by data given on the position of an autowave front propagating through it. It is shown that under certain conditions, this statement of the problem is ill-posed in the sense of the non-uniqueness of the solution. A regularizing approach to its solution was proposed.

中文翻译：

---

用自动波阵面位置上的数据恢复双稳态介质对称状态的反问题的解的非唯一性问题

本文考虑了一个非线性奇异摄动自波动方程逆问题中有可能恢复双稳态介质对称稳态的问题，这是通过传播自波前位置的数据给出的。结果表明，在某些条件下，从解决方案的非唯一性的角度来看，这种对问题的陈述是不恰当的。提出了一种解决其问题的正规化方法。