Asymptotic behavior of solutions to anisotropic conservation laws in two-dimensional space |
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Authors: | Kaiqiang Li |
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Affiliation: | School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240 China |
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Abstract: | 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. |
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Keywords: | anisotropic conservation laws asymptotic behavior Cauchy problem global classical solution rarefaction waves |
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