Asymptotic Time-Behaviour of Solutions to Scalar Conservation Law with a Convex Flux Function
We consider the long-time behaviour of solutions of the Cauchy problem for a quasilinear equation ut + f(u)x = 0 with a strictly convex flux function f(u) and initial function u0(x) having the the one-sided limiting mean values u± that are uniform with respect to translations. The estimates of the r...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2019-01-01
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| Series: | EPJ Web of Conferences |
| Online Access: | https://www.epj-conferences.org/articles/epjconf/pdf/2019/29/epjconf_mnps2018_01005.pdf |
| Summary: | We consider the long-time behaviour of solutions of the Cauchy problem for a quasilinear equation ut + f(u)x = 0 with a strictly convex flux function f(u) and initial function u0(x) having the the one-sided limiting mean values u± that are uniform with respect to translations. The estimates of the rates of convergence to solutions of the Riemann problem depending on the behaviour of the integrals ∫aa+y(u0(x)−u±)dx$ \int\limits_a^{a + y} {\left( {{u_0}\left( x \right) - {u^ \pm }} \right)} dx $ as y→±∞ are established. The similar results are obtained for solutions of the mixed problem in the domain x > 0, t > 0 with a constant boundary data u– and initial data having limiting mean value u±. |
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| ISSN: | 2100-014X |