; Katayose, Y.] Yokohama Natl Univ, Dept Phys, Yokohama, Kanagawa 2408501, Japan
; [Huang, J.] Chinese Acad Sci, Inst High Energy Phys, Key Lab Particle Astrophys, Beijing 100049, Peoples R China
; [Chen, D.] Univ Tokyo, Inst Cosm Ray Res, Kashiwa, Chiba 2778582, Japan
A model of the cosmic-ray energy spectrum is proposed that assumes various acceleration limits at multiple sources. The model describes the broken power-law energy spectrum of cosmic rays by superposition of multiple sources; a diffusive shock acceleration mechanism plays an essential role. The maximum energy of galactic cosmic rays is discussed based on a comparison of experimental data with calculations done using the proposed model. The model can describe the energy spectrum at very high energies of up to several times 10(18) eV, but the observed highest-energy cosmic rays deviate from the model predictions, indicating a different origin, such as an extragalactic source. This model describes the steepening of the power index at the so-called knee. However, it was found that additional assumptions are needed to explain the sharpness of the knee. Two possible explanations for the structure of the knee are discussed in terms of nearby source(s) and the hard energy spectrum suggested by nonlinear effects of cosmic-ray acceleration mechanisms.