Long-time convergence of a nonlocal Burgers' equation towards the local N-wave

被引：3

作者：

Coclite, Giuseppe Maria ^{[1
]}

De Nitti, Nicola ^{[2
]}

Keimer, Alexander ^{[3
]}

Pflug, Lukas ^{[3
,4
]}

Zuazua, Enrique ^{[2
,5
,6
]}

机构：

[1] Polytech Univ Bari, Dept Mech Math & Management, Via E Orabona 4, I-70125 Bari, Italy

[2] Friedrich Alexander Univ Erlangen Nurnberg, Chair Dynam Control Machine Learning & Numer, Dept Math, Alexander Humboldt Professorship, Cauerstr 11, D-91058 Erlangen, Germany

[3] Friedrich Alexander Univ Erlangen Nurnberg, Chair Appl Math Continuous Optimizat, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany

[4] Friedrich Alexander Univ Erlangen Nurnberg, Cent Inst Sci Comp, Martensstr 5a, D-91058 Erlangen, Germany

[5] Fdn Deusto, Chair Computat Math, Ave Univ 24, Bilbao 48007, Basque Country, Spain

[6] Univ Autonoma Madrid, Dept Matemat, Ciudad Univ Cantoblanco, Madrid 28049, Spain

来源：

NONLINEARITY | 2023年 / 36卷 / 11期

关键词：

nonlocal conservation laws; nonlocal flux; Burgers equation; approximation of local conservation laws; N-waves; source-type solutions; entropy solutions; CONVECTION-DIFFUSION EQUATION; ASYMPTOTIC-BEHAVIOR; TRANSPORT-EQUATIONS; CONSERVATION-LAWS; WELL-POSEDNESS; UNIQUENESS; DECAY; LIMIT; MODEL;

D O I：

10.1088/1361-6544/acf01d

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the long-time behaviour of the unique weak solution of a nonlocal regularisation of the (inviscid) Burgers equation where the velocity is approximated by a one-sided convolution with an exponential kernel. The initial datum is assumed to be positive, bounded, and integrable. The asymptotic profile is given by the 'N-wave' entropy solution of the Burgers equation. The key ingredients of the proof are a suitable scaling argument and a nonlocal Oleinik-type estimate.

引用

页码：5998 / 6019

页数：22