A scalar transport equation
A scalar transport equation
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标量传输方程
DOI：
10.1090/s0002-9947-1957-0087880-6
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发表时间：
1957
影响因子：
1.3
通讯作者：
Z. A. Melzak
中科院分区：
文献类型：
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作者：
Z. A. Melzak
这里，变量x、y、t是非负的，并且假定函数f（x，0）、f（x，y）和f#1（x，y）是已知的。主要结果（定理1）是：在对f（x，0），θ（x，y）和yG（x，y）的某些假设下，存在一个连续解f（x，t），对x，t0有效，非负，对每个x在t内解析，对每个f在x内可积。另一个假设保证了唯一性。文[3]从实用的观点出发，讨论了方程（1）的一种特殊形式，即1 0。最近Morgenstern [4]证明了一个存在性定理，它适用于包括方程（1）的情形ImO在内的一般类方程。本文所用的证明方法不仅适用于方程（1），而且也适用于下列形式的某些其它方程：
Here the variables x, y, t are non-negative, and the functions f(x, 0), 4(x, y) and #1(x, y) are assumed to be known. The main result (Theorem 1) is that under certain hypotheses on f(x, 0), 4(x, y) and yG(x, y) there exists a continuous solution f(x, t), valid for x, t_ 0, which is non-negative, analytic in t for each x, and integrable in x for each f. Another hypothesis guarantees uniqueness. A special form of equation (1), with 1 0, was treated from a practical point of view in [3]. More recently an existence theorem has been proved by Morgenstern [4], which applies to a general class of equations including the case ImO of equation (1). The method of proof used in the present paper applies not only to equation (1) but also to certain other equations of the form