Free Access
Issue |
ESAIM: M2AN
Volume 51, Number 1, January-February 2017
|
|
---|---|---|
Page(s) | 225 - 278 | |
DOI | https://doi.org/10.1051/m2an/2016020 | |
Published online | 02 December 2016 |
- E.J. Balder, Lectures on Young measure theory and its applications in economics. Workshop on Measure Theory and Real Analysis (Italian), Grado (1997). Rend. Istit. Mat. Univ. Trieste 31 (2000) 1–69. [Google Scholar]
- C. Bauzet, On a time-splitting method for a scalar conservation law with a multiplicative stochastic perturbation and numerical experiments. J. Evol. Equ. 14 (2014) 333–356. [CrossRef] [MathSciNet] [Google Scholar]
- C. Bauzet, G. Vallet and P. Wittbold, The Cauchy problem for a conservation law with a multiplicative stochastic perturbation. J. Hyperbolic Differ. Eq. 9 (2012) 661–709. [CrossRef] [Google Scholar]
- C. Bauzet, J. Charrier and T. Gallouët, Convergence of flux-splitting finite volume schemes for hyperbolic scalar conservation laws with a multiplicative stochastic perturbation. Math. Comp. 85 (2016) 2777–2813. [CrossRef] [MathSciNet] [Google Scholar]
- C. Bauzet, J. Charrier and T. Gallouët, Convergence of monotone finite volume schemes for hyperbolic scalar conservation laws with a multiplicative noise. Stoch. Partial Differ. Eq. Anal. Comput. 4 (2016) 150–223. [Google Scholar]
- C. Bauzet, G. Vallet and P. Wittbold, The Dirichlet problem for a conservation law with a multiplicative stochastic perturbation. J. Funct. Anal. 4 (2014) 2503–2545. [Google Scholar]
- I.H. Biswas and A.K. Majee, Stochastic conservation laws: Weak-in-time formulation and strong entropy condition. J. Funct. Anal. 7 (2014) 2199–2252. [Google Scholar]
- C. Chainais-Hillairet, Second-order finite-volume schemes for a non-linear hyperbolic equation: error estimate. Math. Methods Appl. Sci. 23 (2000) 467–490. [Google Scholar]
- G.-Q. Chen, Q. Ding and K.H. Karlsen, On nonlinear stochastic balance laws. Arch. Ration. Mech. Anal. 204 (2012) 707–743. [Google Scholar]
- G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions. Vol. 44 of Encycl. Math. Appl. Cambridge University Press, Cambridge (1992). [Google Scholar]
- A. Debussche and J. Vovelle, Scalar conservation laws with stochastic forcing. J. Funct. Anal. 259 (2010) 1014–1042. [Google Scholar]
- R. Eymard, T. Gallouët and R. Herbin, Existence and uniqueness of the entropy solution to a nonlinear hyperbolic equation. Chinese Ann. Math. Ser. B 16 (1995) 1–14. A Chinese summary appears in Chinese Ann. Math. Ser. A 16 (1995) 119. [MathSciNet] [Google Scholar]
- R. Eymard, T. Gallouët and R. Herbin, Finite volume methods. Vol. VII of Handb. Numer. Anal. North-Holland, Amsterdam (2000) 713–1020. [Google Scholar]
- J. Feng and D. Nualart, Stochastic scalar conservation laws. J. Funct. Anal. 255 (2008) 313–373. [Google Scholar]
- M. Hofmanová, Bhatnagar-gross-krook approximation to stochastic scalar conservation laws. Ann. Inst. Henri Poincaré Probab. Statist. (2014). [Google Scholar]
- H. Holden and N.H. Risebro, A stochastic approach to conservation laws. In Third International Conference on Hyperbolic Problems. Vols. I, II (Uppsala, 1990). Studentlitteratur, Lund (1991) 575–587. [Google Scholar]
- K. Kobayasi and D. Noboriguchi, A stochastic conservation law with nonhomogeneous Dirichlet boundary conditions. Acta Math. Vietnam. 41 (2016) 607–632. [CrossRef] [MathSciNet] [Google Scholar]
- I. Kröker and C. Rohde, Finite volume schemes for hyperbolic balance laws with multiplicative noise. Appl. Numer. Math. 62 (2012) 441–456. [Google Scholar]
- F. Otto, Initial-boundary value problem for a scalar conservation law. C. R. Acad. Sci. Paris Sér. I Math. 322 (1996) 729–734. [Google Scholar]
- E. Yu. Panov, On measure-valued solutions of the Cauchy problem for a first-order quasilinear equation. Izv. Ross. Akad. Nauk Ser. Mat. 60 (1996) 107–148. [CrossRef] [MathSciNet] [Google Scholar]
- G. Vallet, Stochastic perturbation of nonlinear degenerate parabolic problems. Differ. Integral Eq. 21 (2008) 1055–1082. [Google Scholar]
- J. Vovelle, Convergence of finite volume monotone schemes for scalar conservation laws on bounded domains. Numer. Math. 90 (2002) 563–596. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.