arXiv math-ph/07020192007-02-06math-phmath.DGmath.MP

数学物理微分方程的特点

Specific features of differential equations of mathematical physics

L. I. Petrova

备注：: 12pages

摘要：

本文研究了三种类型的数学物理方程，即描述任何物理过程的方程、连续介质的力学和物理方程以及场论方程。在第一种和第二种情况下，调查减少到分析的反对称微分形式，从微分方程得到的不相同的关系。证明了方程的可积性及其解的性质依赖于退化变换条件的实现，在退化变换条件下，恒等关系由非恒等关系得到.场论方程与前两类方程相反，是由反对称微分形式或其类似形式（微分或积分形式）构成的关系。这是因为场论方程必须描述物理结构（封闭的外部形式对应于物理结构）而不是物理量。对应于场论的方程是从描述（连续介质的）物质系统的（能量、线动量、角动量和质量）守恒定律的方程中得到的。这揭示了场论和物质系统方程之间的联系（并指出物质介质产生物理场）。

英文摘要：

Three types of equations of mathematical physics, namely, the equations, which describe any physical processes, the equations of mechanics and physics of continuous media, and field-theory equations are studied in this paper. In the first and second case the investigation is reduced to the analysis of the nonidentical relations of the skew-symmetric differential forms that are obtained from differential equations. It is shown that the integrability of equations and the properties of their solutions depend on the realization of the conditions of degenerate transformations under which the identical relations are obtained from the nonidentical relation. The field-theory equations, in contrast to the equations of first two types, are the relations made up by skew-symmetric differential forms or their analogs (differential or integral ones). This is due to the fact that the field-theory equations have to describe physical structures (to which closed exterior forms correspond) rather than physical quantities. The equations that correspond to field theories are obtained from the equations that describe the conservation laws (of energy, linear momentum, angular momentum, and mass) of material systems (of continuous media). This disclose a connection between field theories and the equations for material systems (and points to that material media generate physical fields).

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文