Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws
Biler, Piotr ; Karch, Grzegorz ; Woyczyński, Wojbor A
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001), p. 613-637 / Harvested from Numdam
@article{AIHPC_2001__18_5_613_0,
     author = {Biler, Piotr and Karch, Grzegorz and Woyczy\'nski, Wojbor A},
     title = {Critical nonlinearity exponent and self-similar asymptotics for L\'evy conservation laws},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {18},
     year = {2001},
     pages = {613-637},
     mrnumber = {1849690},
     zbl = {0991.35009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2001__18_5_613_0}
}
Biler, Piotr; Karch, Grzegorz; Woyczyński, Wojbor A. Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) pp. 613-637. http://gdmltest.u-ga.fr/item/AIHPC_2001__18_5_613_0/

[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. | MR 531061 | Zbl 0421.35037

[2] Bertoin J, Lévy Processes, Cambridge University Press, 1996. | MR 1406564 | Zbl 0861.60003

[3] Biler P, Funaki T, Woyczynski W.A, Fractal Burgers equations, J. Differential Equations 148 (1998) 9-46. | MR 1637513 | Zbl 0911.35100

[4] Biler P, Funaki T, Woyczyński W.A, Interacting particle approximation for nonlocal quadratic evolution problems, Prob. Math. Stat. 19 (1999) 267-286. | MR 1750904 | Zbl 0985.60091

[5] Biler P, Karch G, Woyczynski W.A, Asymptotics for multifractal conservation laws, Studia Math. 135 (1999) 231-252. | MR 1708995 | Zbl 0931.35015

[6] Biler P., Karch G., Woyczyński W.A., Asymptotics for conservation laws involving Lévy diffusion generators, preprint. | MR 1881259

[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. | MR 1751668 | Zbl 0945.35015

[8] Biler P, Woyczyński W.A, Global and exploding solutions for nonlocal quadratic evolution problems, SIAM J. Appl. Math. 59 (1999) 845-869. | MR 1661243 | Zbl 0940.35035

[9] Carpio A, Asymptotic behavior for the vorticity equations in dimensions two and three, Comm. PDE 19 (1994) 827-872. | MR 1274542 | Zbl 0816.35108

[10] Carpio A, Large time behaviour in some convection-diffusion equations, Ann. Sc. Norm. Sup. Pisa, ser. IV, 23 (1996) 551-574. | Numdam | MR 1440033 | Zbl 0870.35054

[11] Davies E.B, Heat Kernels and Spectral Theory, Cambridge University Press, 1989. | MR 990239 | Zbl 0699.35006

[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. | MR 1183805 | Zbl 0755.45019

[13] Duro G, Zuazua E, Large time behavior for convection-diffusion equations in RN with asymptotically constant diffusion, Comm. PDE 24 (1999) 1283-1340. | MR 1697489 | Zbl 0931.35068

[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. | MR 1233647 | Zbl 0807.35059

[15] Escobedo M, Vázquez J.L, Zuazua E, A diffusion-convection equation in several space dimensions, Indiana Univ. Math. J. 42 (1993) 1413-1440. | MR 1266100 | Zbl 0791.35059

[16] Escobedo M, Zuazua E, Large time behavior for convection-diffusion equations in RN, J. Funct. Anal. 100 (1991) 119-161. | MR 1124296 | Zbl 0762.35011

[17] Escobedo M, Zuazua E, Long-time behaviour of diffusion waves for a viscous system of conservation laws in RN, Asymptotic Analysis 20 (1999) 133-173. | MR 1700668 | Zbl 0934.35024

[18] Jacob N, Pseudo-Differential Operators and Markov Processes, Akademie Verlag, Berlin, 1996. | MR 1409607 | Zbl 0860.60002

[19] Karch G, Self-similar large time behavior of solutions to Korteweg-de Vries-Burgers equation, Nonlinear Analysis 35 (1999) 199-219. | Zbl 0923.35158

[20] Komatsu T, Uniform estimates for fundamental solutions associated with non-local Dirichlet forms, Osaka J. Math. 32 (1995) 833-860. | MR 1380729 | Zbl 0867.35123

[21] Ladyženskaja O.A, Solonnikov V.A, Ural'Ceva N.N, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc, Providence, RI, 1988. | MR 241822

[22] Mann J.A, Woyczynski W.A, Growing fractal interfaces in the presence of self-similar hopping surface diffusion, Physica A 291 (2001) 159-183. | Zbl 0972.82078

[23] PȩKalski A, Sznajd-Weron K (Eds.), Anomalous Diffusion. From Basics to Applications, Lecture Notes in Physics, 519, Springer-Verlag, Berlin, 1999. | Zbl 0909.00059

[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. | MR 1381481 | Zbl 0823.00016

[25] Simon J, Compact sets in the space Lp(0,T;B), Annali Mat. Pura Appl. 156 (1987) 65-96. | MR 916688 | Zbl 0629.46031

[26] Stroock D.W, Diffusion processes associated with Lévy generators, Z. Wahr. verw. Geb. 32 (1975) 209-244. | MR 433614 | Zbl 0292.60122

[27] Woyczynski W.A, Burgers-KPZ Turbulence - Göttingen Lectures, Lecture Notes in Math., 1700, Springer-Verlag, Berlin, 1998. | Zbl 0919.60004

[28] Zuazua E, Weakly nonlinear large time behavior in scalar convection-diffusion equations, Differential Integral Equations 6 (1993) 1481-1491. | MR 1235206 | Zbl 0805.35054