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Asymptotic behavior of solutions to anisotropic conservation laws in two‐dimensional space
Author(s) -
Li Kaiqiang
Publication year - 2020
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.5941
Subject(s) - conservation law , mathematics , burgers' equation , riemann hypothesis , mathematical analysis , rarefaction (ecology) , space (punctuation) , constant (computer programming) , entropy (arrow of time) , anisotropy , mathematical physics , partial differential equation , physics , ecology , linguistics , philosophy , species diversity , biology , programming language , quantum mechanics , computer science
In this paper, we investigate the asymptotic behavior of solutions for anisotropic conservation laws in two‐dimensional space, provided with step‐like initial conditions that approach the constant states u ± ( u − < u + ) as x →± ∞ , respectively. It shows that there is a global classical solution that converges toward the rarefaction wave, ie, the unique entropy solution of the Riemann problem for the nonviscous Burgers' equation in one‐dimensional space.