Large time behaviour of a conservation law regularised by a Riesz-Feller operator: the sub-critical case

IF 0.4 4区数学 Q4 MATHEMATICS

Czechoslovak Mathematical Journal Pub Date : 2023-02-08 DOI:10.21136/cmj.2023.0235-22

C. M. Cuesta, Xuban Diez

引用次数: 0

Abstract

We study the large time behaviour of the solutions of a non-local regularisation of a scalar conservation law. This regularisation is given by a fractional derivative of order $1+\alpha$, with $\alpha\in(0,1)$, which is a Riesz-Feller operator. The non-linear flux is given by the locally Lipschitz function $|u|^{q-1}u/q$ for $q>1$. We show that in the sub-critical case, $1

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由Riesz-Feller算子正则化的守恒律的大时间行为:次临界情况

研究标量守恒律的非局部正则化解的大时间行为。这个正则化是由阶$1+\alpha$的分数阶导数给出的，其中$\alpha\in(0,1)$，这是一个Riesz-Feller算子。非线性通量由局部Lipschitz函数$|u|^{q-1}u/q$给出。我们证明了在次临界情况下，$1

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