87
Views
2
CrossRef citations to date
0
Altmetric
Article

On the existence of L2-valued thermodynamic entropy solutions for a hyperbolic system with boundary conditions

& ORCID Icon
Pages 1072-1087 | Received 08 Feb 2019, Accepted 17 Jan 2020, Published online: 22 Apr 2020

References

  • Chen, G.-Q., Frid, H. (1999). Vanishing viscosity limit for initial-boundary value problems for conservation laws. Contemp. Math. 238:35–51.
  • Otto, F. (1996). Initial-boundary value problem for a scalar conservation law. C. R. Acad. Sci. Sér. Math. 322:729–734.
  • Evans, L. (2004). A survey of entropy methods for partial differential equations. Bull. Amer. Math. Soc. 41(4):409–438. DOI: 10.1090/S0273-0979-04-01032-8.
  • Ball, J. M., Chen, G.-Q. G. (2013). Entropy and convexity for nonlinear partial differential equations. arXiv preprint arXiv:1310.7975.
  • Serre, D. (1986). La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations á une dimension d’espace. J. Math. Pures Appl. 65(4):423–468.
  • Serre, D., Shearer, J. (1994). Convergence with physical viscosity for nonlinear elasticity. Preprint, unpublished.
  • Shearer, J. W. (1994). Global existence and compactness in Lp for the quasi-linear wave equation. Commun. Partial Differ. Equ. 19(11):1829–1878.
  • Lin, P. (1992). Young measures and an application of compensated compactness to one-dimensional nonlinear elastodynamics. Trans. Amer. Math. Soc. 329(1):377–413. DOI: 10.1090/S0002-9947-1992-1049615-0.
  • Marchesani, S., Olla, S. (2018). Hydrodynamic limit for an anharmonic chain under boundary tension. Nonlinearity. 31(11):4979–5035. DOI: 10.1088/1361-6544/aad675.
  • Marchesani, S., Olla, S. (2020). Hydrodynamic limits and Clausius inequality for isothermal non-linear elastodynamics with boundary tension. arXiv preprint arXiv:1911.13167.
  • Fritz, J. (2011). Microscopic theory of isothermal elastodynamics. Arch. Ration. Mech. Anal. 201(1):209–249. DOI: 10.1007/s00205-010-0385-8.
  • Alasio, L., Marchesani, S. (2019). Global existence for a class of viscous systems of conservation laws. Nonlinear Differ. Equ. Appl. 26(5):32. DOI: 10.1007/s00030-019-0577-3.
  • Marchesani, S. (2020). Hydrodynamic limit for a diffusive system with boundary conditions. arXiv preprint arXiv:1903.08576.
  • Ball, J. M. (1989). A version of the fundamental theorem for young measures. In: Rascle M., Serre D., Slemrod M., eds. PDEs and Continuum Models of Phase Transitions. Vol. 344. Lecture Notes in Physics, Berlin/Heidelberg: Springer, pp. 207–215.
  • Berthelin, F., Vovelle, J. (2017). Stochastic isentropic Euler equations. Anna. ENS (to appear).
  • Dafermos, C. M. (2010). Hyperbolic Conservation Laws in Continuum Physics. Grundlehren Der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Vol. 325, Springer Science & Business Media.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.