BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF FIRST ORDER PSEUDODIFFERENTIAL OPERATORS
BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF FIRST ORDER PSEUDODIFFERENTIAL OPERATORS
复制标题
一阶伪微分算子系统的边值问题
DOI：
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发表时间：
1969
期刊：
影响因子：
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通讯作者：
M. Agranovich
中科院分区：
文献类型：
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作者：
M. Agranovich
本文用一般方法研究了一阶偏微分方程组的一大类问题，在系统（或特征矩阵）对称的假设下，证明了能量不等式定理和弱解与强解的同一性定理，并利用这两个定理证明了强解的存在性和唯一性。这些方法适用于一阶对称双曲型方程组和不一定是椭圆型的对称定常方程组的许多问题。最近，人们发现了利用伪微分算子发展和应用这些方法的新的可能性，目前这些可能性还远远没有穷尽。在§ 1中，对这个问题作了说明，并对文献作了简要的回顾。在§§ 2-6中，给出了上述三个定理，并给出了适用于有界域上一阶伪微分算子系统的证明。§ 7处理可对称化系统的边值问题，比对称系统更一般。
A large group of problems for systems of partial differential equations of the first order is studied by common methods; for these problems the theorem on energy inequalities is proved, under the assumption that the system (or rather, its characteristic matrix) is symmetric, and also the theorem on the identity of the weak and the strong solutions; these two theorems are used to prove existence and uniqueness of the strong solution. The methods are applicable to a number of problems for symmetric hyperbolic systems of the first order and for symmetric stationary systems that need not be elliptic.Recently new possibilities of developing and applying these methods by using pseudodifferential operators have been discovered, and these are far from being exhausted at the present time.In § 1 the problem is stated and a brief survey of the literature is given. In §§ 2-6 the three theorems mentioned above are set out with proofs suitable for systems of pseudodifferential operators of the first order in a bounded domain. § 7 deals with boundary value problems for symmetrizable systems, more general than the symmetric systems.