caa a22 4500 467892849 CHVBK 20180406152754.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10955-005-8006-x doi (NATIONALLICENCE)springer-10.1007/s10955-005-8006-x Scaling Limits of Waves in Convex Scalar Conservation Laws Under Random Initial Perturbations [Elektronische Daten] [Jan Wehr, Jack Xin] We study waves in convex scalar conservation laws under noisy initial perturbations. It is known that the building blocks of these waves are shock and rarefaction waves, both are invariant under hyperbolic scaling. Noisy perturbations can generate complicated wave patterns, such as diffusion process of shock locations. However we show that under the hyperbolic scaling, the solutions converge in the sense of distribution to the unperturbed waves. In particular, randomly perturbed shock waves move at the unperturbed velocity in the scaling limit. Analysis makes use of the Hopf formula of the related Hamilton-Jacobi equation and regularity estimates of noisy processes. Springer Science + Business Media, Inc., 2006 Waves nationallicence Convex scalar conservation laws nationallicence Noise nationallicence Scaling limit nationallicence Wehr Jan Department of Mathematics, University of Arizona, 85721, Tucson, AZ, USA aut Xin Jack Department of Mathematics and ICES, University of Texas at Austin, 78712, Austin, TX, USA aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/2(2006-01-01), 361-370 0022-4715 122:2<361 2006 122 10955 https://doi.org/10.1007/s10955-005-8006-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8006-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wehr Jan Department of Mathematics, University of Arizona, 85721, Tucson, AZ, USA aut NATIONALLICENCE 700 1- Xin Jack Department of Mathematics and ICES, University of Texas at Austin, 78712, Austin, TX, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/2(2006-01-01), 361-370 0022-4715 122:2<361 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer