Abstract

In the article, we examine well-posedness questions in the Sobolev spaces of the inverse source problem in the case of a quasilinear parabolic system of the second order. The main part of the operator is linear. The overdetermination conditions are values of a solution at some collection of interior points. It is demonstrated that, in the case of at most linear growth of the nonlinearity, there exists a unique global (in time) solution and the problem is well-posed in the Sobolev classes. The conditions on the data are minimal and the results are sharp.

中文翻译：

---

一些拟线性抛物系统的点超定逆问题

摘要

在本文中，我们研究了在二阶拟线性抛物系统的情况下，反源问题的Sobolev空间中的适定性问题。运算符的主要部分是线性的。超额确定条件是某个内部点集合的解的值。结果表明，在非线性最多线性增长的情况下，存在唯一的全局（及时）解，并且该问题在Sobolev类中是恰当的。数据条件极少，结果也很清晰。