Two-dimensional fractal Burgers equation with step-like initial conditions

被引：6

作者：

Karch, Grzegorz ^{[1
]}

Pudelko, Anna ^{[2
]}

Xu, Xiaojing ^{[3
]}

机构：

[1] Uniwersytet Wroclawski, Inst Matemat, PL-50384 Wroclaw, Poland

[2] AGH Univ Sci & Technol, PL-30059 Krakow, Poland

[3] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2015年 / 38卷 / 13期

关键词：

fractal Burgers equation; fractional Laplacian; rarefaction waves; self-similar solutions; VISCOUS CONSERVATION-LAWS; RAREFACTION WAVE; ASYMPTOTICS; STABILITY; DIFFUSION;

D O I：

10.1002/mma.3266

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 (c) 2014 John Wiley & Sons, Ltd.

引用

页码：2830 / 2839

页数：10

共 37 条

[11] Global solution and smoothing effect for a non-local regularization of a hyperbolic equation
Droniou, J
Gallouet, T
Vovelle, J
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2003, 3 (03) : 499 - 521
[12] Fractal first-order partial differential equations
Droniou, Jerome
Imbert, Cyril
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2006, 182 (02) : 299 - 331
[13] STABILITY OF VISCOUS SCALAR SHOCK FRONTS IN SEVERAL DIMENSIONS
GOODMAN, J
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 311 (02) : 683 - 695
[14] RAREFACTIONS AND LARGE TIME BEHAVIOR FOR PARABOLIC EQUATIONS AND MONOTONE SCHEMES
HARABETIAN, E
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 114 (04) : 527 - 536
[15] Hattori Y., 1991, JPN J IND APPL MATH, V8, P85, DOI DOI 10.1007/BF03167186
[16] Il'in A.M., 1958, DOKL AKAD NAUK SSSR, V120, P25
[17] Itos K., 1996, MATH MOD METH APPL S, V6, P315
[18] Probabilistic approximation and inviscid limits for one-dimensional fractional conservation laws
Jourdain, B
Méléard, S
Woyczynski, WA
[J]. BERNOULLI, 2005, 11 (04) : 689 - 714
[19] A probabilistic approach for nonlinear equations involving the fractional Laplacian and a singular operator
Jourdain, B
Méléard, S
Woyczynski, WA
[J]. POTENTIAL ANALYSIS, 2005, 23 (01) : 55 - 81
[20] The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations
Ju, N
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2005, 255 (01) : 161 - 181

← 1 2 3 4 →