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- W2024258541 abstract "This is a continuation of [15]. As is well known, one dimensional conservation laws without source term have been extensively investigated after the foundamental paper of J. Glimm [3]. And those with integrable source terms were solved by Liu [6, 7], etc. For higher dimensional case with spherical symmetry, Makino [8] first proved a linear growth rate for solutions when P ( ρ )= σ 2 ρ γ , where γ =1. But in order to get global existence for γ ≠1 and the decay property, we need to find a uniform bound for the approximate solutions. In [15], we introduced a new norm and a functional integral approach to prove a uniform bound for a model problem of Euler equation in R 3 with spherical symmetry. In order to overcome the geometric effects of spherical symmetry which leads to a non-integrable source term, we considered an infinite reflection problem and solved it by considering the cancellations between reflections of different orders. In this paper, we consider a system which describes the isentropic and spherically symmetric motion of gas flow surrounding a solid star with radius 1 and mass M . It is interesting to note that the wave curves for this problem are no longer continuous and there is an extra term in the wave interaction estimates. By introducing a new norm, we prove a similar result as [15]. In the Appendix, we present a local existence theorem for γ ≠1 which was also obtained by Makino [9] by different method. And we extend the results to the cases with different boundary conditions." @default.
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- W2024258541 date "1996-09-01" @default.
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- W2024258541 title "A Functional Integral Approach to Shock Wave Solutions of the Euler Equations with Spherical Symmetry (II)" @default.
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- W2024258541 doi "https://doi.org/10.1006/jdeq.1996.0137" @default.
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