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Smooth solutions for one‐dimensional relativistic radiation hydrodynamic equations
Author(s) -
Geng Yongcai,
Jiang Peng
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3422
Subject(s) - mathematics , eigenvalues and eigenvectors , contraction mapping , contraction (grammar) , banach space , energy method , scheme (mathematics) , mathematical analysis , physics , fixed point , medicine , quantum mechanics
In this research article, we investigated the existence of local smooth solutions for relativistic radiation hydrodynamic equations in one spatial variable. The proof is based on a classical iteration method and the Banach contraction mapping principle. However, because of the complexity of relativistic radiation hydrodynamics equations, we first rewrite this system into a semilinear form to construct the iteration scheme and then use left eigenvectors to decouple the system instead of applying standard energy method on symmetric hyperbolic systems. Different from multidimensional case, we just use the characteristic method, which can keep the properties of the initial data. Copyright © 2015 John Wiley & Sons, Ltd.