WANG, Xian-Ting. Global Solutions to Isothermal System with Source. []. , 39, 1, pp.51-55.   28--2021. ISSN 0120-419X.  https://doi.org/10.18273/revint.v39n1-2021004.

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In this short note, we are concerned with the global existence of solutions to the isothermal system with source, where the inhomogeneous terms f(x, t, ρ, u) = b(x, t)ρ + ρu2 + α(x, t)ρu|u| are appeared in the momentum equation. Our work extended the results in the previous papers “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) and “Existence of Global Solutions for Isentropic Gas Flow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the global solution was obtained for the source f(x, t, ρ, u) = ρu2 , f(x, t, ρ, u) = b(x, t)ρ, f(x, t, ρ, u) = α(x, t)ρu|u| respectively.

En esta nota estamos interesados en la existencia global de soluciones para el sistema isotérmico con fuente, donde los términos no homogéneos f(x, t, ρ, u) = b(x, t)ρ + 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 solución global se obtuvo, respectivamente, para las fuentes f(x, t, ρ, u) = ρu2 , f(x, t, ρ, u) = b(x, t)ρ and f(x, t, ρ, u) = α(x, t)ρu|u|.

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