Asymptotic behavior of solutions to scalar conservation laws and optimal convergence orders to N-waves |
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Authors: | Yong Jung Kim |
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Affiliation: | Impedance Imaging Research Center, Kyunghee University, Kyunggi 449-701, South Korea |
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Abstract: | The goal of this article is to develop a new technique to obtain better asymptotic estimates for scalar conservation laws. General convex flux, f″(u)?0, is considered with an assumption . We show that, under suitable conditions on the initial value, its solution converges to an N-wave in L1 norm with the optimal convergence order of O(1/t). The technique we use in this article is to enclose the solution with two rarefaction waves. We also show a uniform convergence order in the sense of graphs. A numerical example of this phenomenon is included. |
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Keywords: | Asymptotics Characteristics Convergence order N-wave Similarity |
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