Details

Autor(en) / Beteiligte

• Guelmame, Billel
• Houamed, Haroune

Titel

Convergence rate for a regularized scalar conservation law

Ist Teil von

• Zeitschrift für angewandte Mathematik und Physik, 2024, Vol.75 (3)

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2024

Link zum Volltext

Quelle

SpringerLink (Online service)

Beschreibungen/Notizen

• This work revisits a recent finding by the first author concerning the local convergence of a regularized scalar conservation law. We significantly improve the original statement by establishing a global convergence result within the Lebesgue spaces L loc ∞ ( R + ; L p ( R ) ) , for any p ∈ [ 1 , ∞ ) , as the regularization parameter ℓ approaches zero. Notably, we demonstrate that this stability result is accompanied by a quantifiable rate of convergence. A key insight in our proof lies in the observation that the fluctuations of the solutions remain under control in low regularity spaces, allowing for a potential quantification of their behavior in the limit as ℓ → 0 . This is achieved through a careful asymptotic analysis of the perturbative terms in the regularized equation, which, in our view, constitutes a pivotal contribution to the core findings of this paper.