标题： 不适定Cauchy问题的数值解法，针对拟线性抛物型方程使用Carleman权函数 显示英文标题

标题： Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function

摘要： 这是首次发表的关于用严格方法数值求解拟线性偏微分方程不适定Cauchy问题的论文。 更准确地说，我们解决了1维拟线性抛物型方程的侧面Cauchy问题。 关键思想是在目标泛函中引入Carleman加权函数并最小化一个严格凸的目标泛函。 先前关于不适定Cauchy问题数值解的出版物仅考虑了线性方程。 显示英文摘要

摘要： This is the first publication in which an ill-posed Cauchy problem for a quasi- linear PDE is solved numerically by a rigorous method. More precisely, we solve the side Cauchy problem for a 1-d quasilinear parabolc equation. The key idea is to minimize a strictly convex cost functional with the Carleman Weight Function in it. Previous publications about numerical solutions of ill-posed Cauchy problems were considering only linear equations.