TY - JOUR
T1 - Conservation laws with discontinuous gradient-dependent flux
T2 - The stable case
AU - Amadori, Debora
AU - Bressan, Alberto
AU - Shen, Wen
N1 - Publisher Copyright:
© World Scientific Publishing Company.
PY - 2025/6/1
Y1 - 2025/6/1
N2 - This paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions f(u) or g(u), when the gradient ux of the solution is positive or negative, respectively. We study here the stable case where f(u) < g(u) for all u ∈ R, with f, g smooth but possibly not convex. A front tracking algorithm is introduced, proving that piecewise constant approximations converge to the trajectories of a contractive semigroup on L1(R). In the spatially periodic case, we prove that semigroup trajectories coincide with the unique limits of a suitable class of vanishing viscosity approximations.
AB - This paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions f(u) or g(u), when the gradient ux of the solution is positive or negative, respectively. We study here the stable case where f(u) < g(u) for all u ∈ R, with f, g smooth but possibly not convex. A front tracking algorithm is introduced, proving that piecewise constant approximations converge to the trajectories of a contractive semigroup on L1(R). In the spatially periodic case, we prove that semigroup trajectories coincide with the unique limits of a suitable class of vanishing viscosity approximations.
UR - https://www.scopus.com/pages/publications/105001593302
UR - https://www.scopus.com/inward/citedby.url?scp=105001593302&partnerID=8YFLogxK
U2 - 10.1142/S0218202525500216
DO - 10.1142/S0218202525500216
M3 - Article
AN - SCOPUS:105001593302
SN - 0218-2025
VL - 35
SP - 1421
EP - 1469
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 6
ER -