A Class Existence And Uniqueness Of The Leakage Model Of The Attenuation Coefficient,

Nowadays, the detection of the position and the intensity and the decline coefficient in the leakage model of the pipeline net of gas(oil), especially the detection of the position is the most popular problem in the research of engineering project and theory of preservation and transportation, and at the same time the problem in practice of the manufacture of the oil field. Many engineer and natural science workers in internal and overseas pay close attention to this difficult problem, and do their best to resolve it. During recent twenty to thirty years, there has been a great many of achievement, as well models and methods, which focus to find a fairly easy way of detecting the position and intensity and the decline coefficient of the leaks in the pipeline net of gas (oil) and other relative quantity. One kind of the models which are being researched are the simple models set up on the base of stable condition, they have a larger error in detection, so they can not suffice to engineering. The other kind of the models are the unlinear partial differential equation group which set up from move equation, sequential equation, and condition equation. We used all kinds of numerical calculation means to seek the position and intensity and the decline coefficient of the leaks in pipeline net, but the precisions are not high, and the effects are not satisfactory. Many overseas large-size petroleum company have developed some examination software, they keep their technology secret and the software is very expensive. Therefore, it stimulates strongly the confidence of countrymen to research the detection of the leaks in the pipeline net.In this paper, on the base of [10][12], we use a method to make the unlinear partial differential equation group which described the move in the pipeline net of gas(oil) to be linear, and set up a linear partial differential equation model to describe the single-leak in the pipeline net of gas(oil) in the examine stage [contain the position and the intensity(constant 1) and the decline coefficient of the leaks] for the first time. And then use the theory of inverse problem of partial deferential equation, select some feasible means of measurement and data, added some additional conditions...