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Remarks on the derivation of several second order partial differential equations from a generalization of the Einstein equations. (English) Zbl 1441.35232

Summary: 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.

MSC:

35Q75 PDEs in connection with relativity and gravitational theory
35G20 Nonlinear higher-order PDEs
35Q76 Einstein equations
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