Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws
Piotr Biler; Grzegorz Karch; Wojbor A Woyczyński
Annales de l'I.H.P. Analyse non linéaire (2001)
- Volume: 18, Issue: 5, page 613-637
- ISSN: 0294-1449
Access Full Article
topHow to cite
topBiler, Piotr, Karch, Grzegorz, and Woyczyński, Wojbor A. "Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws." Annales de l'I.H.P. Analyse non linéaire 18.5 (2001): 613-637. <http://eudml.org/doc/78532>.
@article{Biler2001,
author = {Biler, Piotr, Karch, Grzegorz, Woyczyński, Wojbor A},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {generalized Burgers equation; Lévy diffusion; anomalous diffusion},
language = {eng},
number = {5},
pages = {613-637},
publisher = {Elsevier},
title = {Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws},
url = {http://eudml.org/doc/78532},
volume = {18},
year = {2001},
}
TY - JOUR
AU - Biler, Piotr
AU - Karch, Grzegorz
AU - Woyczyński, Wojbor A
TI - Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 5
SP - 613
EP - 637
LA - eng
KW - generalized Burgers equation; Lévy diffusion; anomalous diffusion
UR - http://eudml.org/doc/78532
ER -
References
top- [1] Bardos C, Penel P, Frisch U, Sulem P.L, Modified dissipativity for a nonlinear evolution equation arising in turbulence, Arch. Rat. Mech. Anal.71 (1979) 237-256. Zbl0421.35037MR531061
- [2] Bertoin J, Lévy Processes, Cambridge University Press, 1996. Zbl0861.60003MR1406564
- [3] Biler P, Funaki T, Woyczynski W.A, Fractal Burgers equations, J. Differential Equations148 (1998) 9-46. Zbl0911.35100MR1637513
- [4] Biler P, Funaki T, Woyczyński W.A, Interacting particle approximation for nonlocal quadratic evolution problems, Prob. Math. Stat.19 (1999) 267-286. Zbl0985.60091MR1750904
- [5] Biler P, Karch G, Woyczynski W.A, Asymptotics for multifractal conservation laws, Studia Math.135 (1999) 231-252. Zbl0931.35015MR1708995
- [6] Biler P., Karch G., Woyczyński W.A., Asymptotics for conservation laws involving Lévy diffusion generators, preprint. Zbl0990.35023MR1881259
- [7] Biler P, Karch G, Woyczyński W.A, Multifractal and Lévy conservation laws, C. R. Acad. Sci. Paris, Sér. I Math.330 (2000) 343-348. Zbl0945.35015MR1751668
- [8] Biler P, Woyczyński W.A, Global and exploding solutions for nonlocal quadratic evolution problems, SIAM J. Appl. Math.59 (1999) 845-869. Zbl0940.35035MR1661243
- [9] Carpio A, Asymptotic behavior for the vorticity equations in dimensions two and three, Comm. PDE19 (1994) 827-872. Zbl0816.35108MR1274542
- [10] Carpio A, Large time behaviour in some convection-diffusion equations, Ann. Sc. Norm. Sup. Pisa, ser. IV,23 (1996) 551-574. Zbl0870.35054MR1440033
- [11] Davies E.B, Heat Kernels and Spectral Theory, Cambridge University Press, 1989. Zbl0699.35006MR990239
- [12] Duoandikoetxea J, Zuazua E, Moments, masses de Dirac et décomposition de fonctions, C. R. Acad. Sci. Paris, Sér. I Math.315 (1992) 693-698. Zbl0755.45019MR1183805
- [13] Duro G, Zuazua E, Large time behavior for convection-diffusion equations in RN with asymptotically constant diffusion, Comm. PDE24 (1999) 1283-1340. Zbl0931.35068MR1697489
- [14] Escobedo M, Vázquez J.L, Zuazua E, Asymptotic behaviour and source-type solutions for a diffusion-convection equation, Arch. Rat. Mech. Anal.124 (1993) 43-65. Zbl0807.35059MR1233647
- [15] Escobedo M, Vázquez J.L, Zuazua E, A diffusion-convection equation in several space dimensions, Indiana Univ. Math. J.42 (1993) 1413-1440. Zbl0791.35059MR1266100
- [16] Escobedo M, Zuazua E, Large time behavior for convection-diffusion equations in RN, J. Funct. Anal.100 (1991) 119-161. Zbl0762.35011MR1124296
- [17] Escobedo M, Zuazua E, Long-time behaviour of diffusion waves for a viscous system of conservation laws in RN, Asymptotic Analysis20 (1999) 133-173. Zbl0934.35024MR1700668
- [18] Jacob N, Pseudo-Differential Operators and Markov Processes, Akademie Verlag, Berlin, 1996. Zbl0860.60002MR1409607
- [19] Karch G, Self-similar large time behavior of solutions to Korteweg–de Vries–Burgers equation, Nonlinear Analysis35 (1999) 199-219. Zbl0923.35158
- [20] Komatsu T, Uniform estimates for fundamental solutions associated with non-local Dirichlet forms, Osaka J. Math.32 (1995) 833-860. Zbl0867.35123MR1380729
- [21] Ladyženskaja O.A, Solonnikov V.A, Ural'ceva N.N, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc, Providence, RI, 1988. MR241822
- [22] Mann J.A, Woyczynski W.A, Growing fractal interfaces in the presence of self-similar hopping surface diffusion, Physica A291 (2001) 159-183. Zbl0972.82078
- [23] Pȩkalski A, Sznajd-Weron K (Eds.), Anomalous Diffusion. From Basics to Applications, Lecture Notes in Physics, 519, Springer-Verlag, Berlin, 1999. Zbl0909.00059
- [24] Shlesinger M.F, Zaslavsky G.M, Frisch U (Eds.), Lévy Flights and Related Topics in Physics, Lecture Notes in Physics, 450, Springer-Verlag, Berlin, 1995. Zbl0823.00016MR1381481
- [25] Simon J, Compact sets in the space Lp(0,T;B), Annali Mat. Pura Appl.156 (1987) 65-96. Zbl0629.46031MR916688
- [26] Stroock D.W, Diffusion processes associated with Lévy generators, Z. Wahr. verw. Geb.32 (1975) 209-244. Zbl0292.60122MR433614
- [27] Woyczynski W.A, Burgers–KPZ Turbulence – Göttingen Lectures, Lecture Notes in Math., 1700, Springer-Verlag, Berlin, 1998. Zbl0919.60004
- [28] Zuazua E, Weakly nonlinear large time behavior in scalar convection-diffusion equations, Differential Integral Equations6 (1993) 1481-1491. Zbl0805.35054MR1235206
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.