关于地球物理中几个不适定问题的解的连续依赖性

本文讨论地球物理资料解释中三类典型的不适定问题,主要内容如下: 1.综述与三类典型不适定问题有关的问题及研究概况; 2.建立一个更接近物理实际的不适定问题的新提法; 3.给出三类典型不适定问题解的Hlder连续依赖性的估计式。

ON THE CONTINUOUS DEPENDENCE OF THE SOLUTIONS FOR SEVERAL IMPROPERLY POSED PROBLEMS IN GEOPHYSICS

This paper discusses three kinds of typical improperly posed problems in interpretation of geophysical informations, i.e., Cauchy's problem for Laplace's equation, time-directional Cauehy's problem for wave equation and Cauehy's problem for the equation of heat conduction. The main contents are presented as follows:1. We state succinctly the questions in relation to three kinds of typical improperly posed problems and pay spacial attention to several points when solving these problems.2. We establish a new formulation of definite problem more close to physical practice and give an estimate of the continuous dependence of its solutions.3. We give the estimates of Holder continuous dependence of the solutions for three kinds of typical improperly posed problems.