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Soluciones globales para sistema isotérmico con fuente.

  • Autores: Xian Ting Wang
  • Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 39, Nº. 1, 2021, págs. 51-55
  • Idioma: español
  • DOI: 10.18273/revint.v39n1-2021004
  • Enlaces
  • Resumen
    • español

      En esta nota estamos interesados en la existencia global de soluciones para el sistema isot\'ermico con fuente, donde los términos no homog\'eneos f(x, t, ρ, u) = b(x, t)ρ +\dfrac{a'(x)}{a(x)}+ρu2 + α(x, t)ρu|u| aparecen en la ecuación de momento. Nuestros resultados extienden los presentados en ``Resonance for the Isothermal System of Isentropic Gas Dynamics'' (Proc. A.M.S.139(2011),2821-2826), ``Global Existence and Stability to the Polytropic Gas Dynamics with an Outer Force'' (Appl. Math. Letters, 95(2019), 35-40) y ``Existence of Global Solutions for Isentropic Gas Flow with Friction'' (Nonlinearity, 33(2020), 3940-3969), en los cuales la soluci\'on global se obtuvo, respectivamente, para las fuentes f(x, t, ρ, u) = \dfrac{a'(x)}{a(x)}+ρu2, f(x, t, ρ, u) = b(x, t)ρ, f(x, t, ρ, u) = α(x, t)ρu|u|.

    • English

      In this short note, we are concerned with the global existenceof solutions to the isothermal system with source, where the inhomoge-neous termsf(x,t,ρ,u) =b(x,t)ρ+a′(x)a(x)ρu2+α(x,t)ρu|u|are appearedin the momentum equation. Our work extended the results in the previ-ous papers “Resonance for the Isothermal System of Isentropic Gas Dynam-ics” (Proc. A.M.S.139(2011),2821-2826), “Global Existence and Stability tothe Polytropic Gas Dynamics with an Outer Force” (Appl. Math. Let-ters, 95(2019), 35-40) and “Existence of Global Solutions for Isentropic GasFlow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the globalsolution was obtained for the sourcef(x,t,ρ,u) =a′(x)a(x)ρu2,f(x,t,ρ,u) =b(x,t)ρ,f(x,t,ρ,u) =α(x,t)ρu|u|respectively.

  • Referencias bibliográficas
    • Referencias Cao W.-T., Huang F.-M. and Yuan D.-F., “Global Entropy Solutions to the Gas Flow in General Nozzle”, SIAM. Journal on Math....
    • Chen G.-Q. and Glimm J., “Global solutions to the compressible Euler equations with geometric structure”, Commun. Math. Phys 180 (1996), 153-193....
    • Hu Y.-B, Lu Y.-G. and Tsuge N., “Global Existence and Stability to the Polytropic Gas Dynamics with an Outer Force”, Appl. Math. Lett, 95...
    • Huang F.-M. and Wang Z., “Convergence of Viscosity Solutions for Isentropic Gas Dynamics”, SIAM J. Math. Anal, 34 (2003), 595-610.doi: 10.1137/S0036141002405819
    • Lu Y.-G., “Existence of Global Solutions for Isentropic Gas Flow with Friction”, Nonlinearity, 33 (2020), No 8, 3940-3969. doi:10.1088/1361-6544/ab7d20
    • Lu Y.-G., Hyperbolic Conservation Laws and the Compensated Compactness Method, Chapman and Hall, vol. 128, Boca Ratón, 2002.
    • Lu Y.-G., “Resonance for the isothermal system of isentropic gas dynamics”, Proc. A.M.S., 139 (2011), 2821-2826. doi: 10.1090/S0002-9939-2011-10733-0
    • Tsuge N., “Existence and Stability of Solutions to the Compressible Euler Equations with an Outer Force”, Nonlinear Analysis, Real World Applications,...
    • Tsuge N., “Isentropic Gas Flow for the Compressible Euler Equations in a Nozzle”, Arch. Rat. Mech. Anal, 209 (2013), No. 2, 365-400. doi:...

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