Two‐dimensional fractal Burgers equation with step‐like initial conditions |
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| Authors: | Grzegorz Karch Anna Pude?ko Xiaojing Xu |
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| Affiliation: | 1. Instytut Matematyczny, Uniwersytet Wroc?awski, pl. Grunwaldzki 2/4, 50‐384 Wroc?aw, Poland;2. AGH University of Science and Technology, al. Mickiewicza 30, 30‐059 Kraków, Poland;3. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China |
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| Abstract: | We consider the two‐dimensional convection–diffusion equation with a fractional Laplacian, supplemented with step‐like initial conditions. We show that the large time behavior of solutions to this IVP is described either by rarefaction waves, or diffusion waves, or suitable self‐similar solutions, depending on the order of the fractional dissipation and on a direction of a convective nonlinearity. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | fractal Burgers equation fractional Laplacian rarefaction waves self‐similar solutions |
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