Global weak solutions for a 2 × 2 balance non-symmetric system of Keyfitz-Kranzer type / Soluciones débiles globales para un sistema 2x2 balanceado no simétrico de tipo Keyfitz-Kranzer

Contenido principal del artículo

Autores

Juan Carlos Juajibioy Otero http://orcid.org/0000-0003-4478-5201
Richard Alexander De La Cruz Guerrero
Leonardo Rendón Arbeláez

Resumen

In this paper we consider the Cauchy problem for a particular non-symmetric Keyfitz-Kranzer type system,
by using the vanishing viscosity method coupled with the compensated compactness method we get global
bounded entropy weak solutions. The main difficulty is to get uniformly bounded estimates on the viscosity
method.

Detalles del artículo

Referencias

[1] H. Cheng. Delta shock waves for a linearly degenerate hyperbolic systems of conservation laws of Keyfitz-Kranzer type. Adv. Math. Phys., 2013:1–10, 2013.

[2] P. Bagnerini , R.M. Colombo , A. Corli. On the role of source terms in continuum traffic flow models. Math. Comput. Modelling, 44:917 -930, 2006.

[3] R.M. Colombo, A. Corli. Well-posedness for multiline traffic models. Ann. Univ. Ferrara., VII:291–301, 2006.

[4] Ito K. Weak solutions to the one-dimensional non-isentropic gas dynamics by the vanishing viscosity method. Electronic Journal of Differential Equations, 1996(4):1–17, 1996.

[5] S. N. Kruzkov. First order quasilinear equations with several space variables. Math. USSRSB, 10:217–243, 1970.

[6] R. De la cruz. Well-posedness to the cauchy problem associated to the non-linear schröndinger equation. Ciencia en Desarrollo, 4 (1):103–113, 2014.

[7] L.Gosse. Analyse et approximation numerique de systemes hyperboliques de lois de conservation avec termes sources. application aux equations dEuler et a un modele simplifie decoulements diphasiques. PhD thesis, Universite Paris ix Dauphine UFR, 1998.

[8] Y. Lu. Existence of global entropy solutions to general systems of Keyfitz-Kranzer type. J. Funct. Anal., 264:2457–2468, 2013.

[9] Juan C. Juajibioy R. De la cruz and Leonardo Rendón. Relaxation limit for aw-rascle system. J. Part. Diff. Eq., 27(2):166–175, 2014.

[10] J.A. Smoller. Shock Waves and Reaction- Diffusion Equations. Springer-Verlag, 1994.

[11] B. Temple. Global solutions of the Cauchy problem for a class of 22 non-strictly hyperbolic conservation laws. Adv. in Appl. Math.,
3:335–375, 1982.

[12] H. Cheng, H. Yang. On a nonsymmetric Keyfitz-Kranzer system of conservation laws with generalized and modified Chaplygin gas pressure law. Adv. Math. Phys., 2013:1–14, 2013.

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