1. Convergence rate for a regularized scalar conservation law.
- Author
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Guelmame, Billel and Houamed, Haroune
- Subjects
CONSERVATION laws (Physics) ,REGULARIZATION parameter ,CONSERVATION laws (Mathematics) - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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