Geodesic
Uniqueness for stochastic scalar conservation laws on Riemannian manifolds revisited
Filomat, Tome 36 (2022) no. 5, p. 1615

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DOI

We revise a uniqueness question for the scalar conservation law with stochastic forcing du + divɡ f(x, u)dt = Φ(x, u)dW t , x ∈ M, t ≥ 0 on a smooth compact Riemannian manifold (M,) where W t is the Wiener process and x → f(x, ξ) is a vector field on M for each ξ ∈ R. We introduce admissibility conditions, derive the kinetic formulation and use it to prove uniqueness in a more straightforward way than in the existing literature.
DOI : 10.2298/FIL2205615K
Classification : 35K65, 42B37, 76S99
Keywords: conservation laws, stochastic, Cauchy problem, Riemannian manifold, kinetic formulation, uniqueness 
Nikola Konatar. Uniqueness for stochastic scalar conservation laws on Riemannian manifolds revisited. Filomat, Tome 36 (2022) no. 5, p. 1615 . doi: 10.2298/FIL2205615K
@article{10_2298_FIL2205615K,
     author = {Nikola Konatar},
     title = {Uniqueness for stochastic scalar conservation laws on {Riemannian} manifolds revisited},
     journal = {Filomat},
     pages = {1615 },
     year = {2022},
     volume = {36},
     number = {5},
     doi = {10.2298/FIL2205615K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2205615K/}
}
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