Publicado

2006-01-01

Existence of global entropy solutions to a non-strictly hyperbolic system with a source

Palabras clave:

Entropy solution, Kinetic formulation, The maximum principle, 2000 Mathematics Subject Classification, Primary: 35D05 (en)

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Autores/as

  • Rei-Fang Yang University of Aeronautics & Astronautics, China

Abstract. In this paper we use the theory of compensated compactness coupled with some basic ideas of the Kinetic formulation to establish an existence theorem for global entropy solutions to the non-strictly hyperbolic system with a source.

                 ρ t + (ρ u)x   = U (ρ,u,x,t)

  ut + (u2/2 + P (ρ))x     =  V (ρ,u,x,t)

En este artículo usamos la teoría de la compacidad compensada asociada con algunas ideas básicas de formulación Kinetica para establecer un teorema de existencia para soluciones de entropía global del sistema no estrictamente hiperbólico con fuente.

               ρ t + (ρ u)x   = U (ρ,u,x,t)

ut + (u2/2 + P (ρ))x     =  V (ρ,u,x,t)

Referencias

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J. Glimm, Solutions in the large for nonliear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 95-105.

C. Klingenberg & Y.- G. Lu, Existence of solutions to hyperbolic conservation Laws with a source, Commun. Math. Phys. 187 (1997), 327-340.

P. L. Lions, B. Perthame & P. E. Souganidis, Existence and stabibility of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Comm. Pure Appl. Math. 4 9 (1996), 599-638.

P. L. Lions, B. Perthame & E. Tadmor, Kinetic formulation of the isentropic gas dynamics and p-system, Comm. Pure Appl. Math. 163 (1994), 415-431.

T. P. Liu, Quasilinear hyperbolic systems, Commn. Math. Phys. 68 (1979), 141-172.

Y. -G. Lu, Convergence of the viscosity method for nonstrictly hyperbolic conservation laws, Commun. Math. Phys. 150 (1992), 59-64.

Y. G. Lu, Existence of generalized solutions for some coupled system of nonlinear hyperbolic equations, J. Sys. Sci. & Math. Scis. 16 (1996) (in Chineses), 125-135.

Y. -G. Lu, Hyperbolic Conservation Laws and the Compensated Compactness Method, Chapman and Hall, CRC Press, New York, 2002.

Y. -G. Lu, Existence of global entropy solutions to a nonstrictly hyperbolic system, Arch. Rat. Mech. Anal. 178 (2005), 287-299.

Cómo citar

APA

Yang, R.-F. (2006). Existence of global entropy solutions to a non-strictly hyperbolic system with a source. Revista Colombiana de Matemáticas, 40(1), 53–64. https://revistas.unal.edu.co/index.php/recolma/article/view/94671

ACM

[1]
Yang, R.-F. 2006. Existence of global entropy solutions to a non-strictly hyperbolic system with a source. Revista Colombiana de Matemáticas. 40, 1 (ene. 2006), 53–64.

ACS

(1)
Yang, R.-F. Existence of global entropy solutions to a non-strictly hyperbolic system with a source. rev.colomb.mat 2006, 40, 53-64.

ABNT

YANG, R.-F. Existence of global entropy solutions to a non-strictly hyperbolic system with a source. Revista Colombiana de Matemáticas, [S. l.], v. 40, n. 1, p. 53–64, 2006. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/94671. Acesso em: 22 ene. 2025.

Chicago

Yang, Rei-Fang. 2006. «Existence of global entropy solutions to a non-strictly hyperbolic system with a source». Revista Colombiana De Matemáticas 40 (1):53-64. https://revistas.unal.edu.co/index.php/recolma/article/view/94671.

Harvard

Yang, R.-F. (2006) «Existence of global entropy solutions to a non-strictly hyperbolic system with a source», Revista Colombiana de Matemáticas, 40(1), pp. 53–64. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/94671 (Accedido: 22 enero 2025).

IEEE

[1]
R.-F. Yang, «Existence of global entropy solutions to a non-strictly hyperbolic system with a source», rev.colomb.mat, vol. 40, n.º 1, pp. 53–64, ene. 2006.

MLA

Yang, R.-F. «Existence of global entropy solutions to a non-strictly hyperbolic system with a source». Revista Colombiana de Matemáticas, vol. 40, n.º 1, enero de 2006, pp. 53-64, https://revistas.unal.edu.co/index.php/recolma/article/view/94671.

Turabian

Yang, Rei-Fang. «Existence of global entropy solutions to a non-strictly hyperbolic system with a source». Revista Colombiana de Matemáticas 40, no. 1 (enero 1, 2006): 53–64. Accedido enero 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/94671.

Vancouver

1.
Yang R-F. Existence of global entropy solutions to a non-strictly hyperbolic system with a source. rev.colomb.mat [Internet]. 1 de enero de 2006 [citado 22 de enero de 2025];40(1):53-64. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/94671

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