从爱因斯坦方程的推广推导出几个二阶偏微分方程

IF 0.5 4区数学 Q3 MATHEMATICS

Osaka Journal of Mathematics Pub Date : 2020-04-01 DOI:10.18910/75916

Makoto Nakamura

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引用次数: 3

摘要

对复线元考虑了带宇宙学常数的爱因斯坦方程的推广。在齐次和各向同性空间中，以半线性场方程的形式导出了若干二阶半线性偏微分方程。本文还考虑了场方程的非相对论性极限。基于场方程的能量估计，研究了空间膨胀和收缩的性质。讨论了几个耗散和反耗散性质。

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REMARKS ON THE DERIVATION OF SEVERAL SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS FROM A GENERALIZATION OF THE EINSTEIN EQUATIONS

A generalization of the Einstein equations with the cosmological constant is considered for complex line elements. Several second order semilinear partial differential equations are derived from them as semilinear field equations in homogeneous and isotropic spaces. The nonrelativistic limits of the field equations are also considered. The properties of spatial expansion and contraction are studied based on energy estimates of the field equations. Several dissipative and anti-dissipative properties are remarked.

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来源期刊

Osaka Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Osaka Journal of Mathematics is published quarterly by the joint editorship of the Department of Mathematics, Graduate School of Science, Osaka University, and the Department of Mathematics, Faculty of Science, Osaka City University and the Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University with the cooperation of the Department of Mathematical Sciences, Faculty of Engineering Science, Osaka University. The Journal is devoted entirely to the publication of original works in pure and applied mathematics.