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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 10
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Research Article

Blow-up of solutions to a scalar conservation law with nonlocal source arising in radiative gas

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Pages 1751-1756 | Received 08 Feb 2023, Accepted 06 Jul 2023, Published online: 27 Sep 2023

References

  • Hamer K. Non-linear effects on the propagation of sound waves in a radiating gas. Q J Mech Appl Math. 1971;24(2):155–168. doi: 10.1093/qjmam/24.2.155
  • Lattanzio C, Marcati P. Global well-posedness and relaxation limits of a model for radiating gas. J Differ Equ. 2003;190(2):439–465. doi: 10.1016/S0022-0396(02)00158-4
  • Yang T, Zhao H. BV estimates on Lax-Friedrichs' scheme or a model of radiating gas. Appl Anal. 2004;83(5):533–539. doi: 10.1080/00036810410001649674
  • Schochet S, Tadmor E. Regularized Chapman-Enskog expansion for scalar conservation laws. Arch Ration Mech Anal. 1992;119:95–107. doi: 10.1007/BF00375117
  • Kawashima S, Nishibata S. Cauchy problem for a model system of the radiating gas: weak solutions with a jump and classical solutions. Math Models Methods Appl Sci. 1999;9(01):69–91. doi: 10.1142/S0218202599000063
  • Kawashima S, Nikkuni Y, Nishibata S. The initial value problem for hyperbolic-elliptic coupled systems and applications to radiation hydrodynamics. Anal Syst Conserv Laws. 1998;99:87–127.
  • Li K, Ruan L, Yang A. Periodic entropy solution to a conservation law with nonlocal source arising in radiative gas. J Math Anal Appl. 2022;512(1):1–17.
  • Di Francesco M, Lattanzio C. Optimal L1 rate of decay to diffusion waves for the Hamer model of radiating gases. Appl Math Lett. 2006;19(10):1046–1052. doi: 10.1016/j.aml.2004.11.008
  • Iguchi T, Kawashima S. On space-time decay properties of solutions to hyperbolic-elliptic coupled systems. Hiroshima Math J. 2002;32(2):229–308. doi: 10.32917/hmj/1151007559
  • Kawashima S, Nishibata S. Shock waves for a model system of the radiating gas. SIAM J Math Anal. 1998;30(1):95–117. doi: 10.1137/S0036141097322169
  • Kawashima S, Tanaka Y. Stability of rarefaction waves for a model system of a radiating gas. Kyushu J Math. 2004;58(2):211–250. doi: 10.2206/kyushujm.58.211
  • Nishibata S. Asymptotic behavior of solutions to a model system of radiating gas with discontinuous initial data. Math Models Methods Appl Sci. 2000;10(08):1209–1231. doi: 10.1142/S0218202500000598
  • Ruan L, Zhang J. Asymptotic stability of rarefaction wave for hyperbolic-elliptic coupled system in radiating gas. Acta Math Sci. 2007;27(2):347–360. doi: 10.1016/S0252-9602(07)60035-6
  • Ruan L, Zhu C J. Asymptotic decay toward rarefaction wave for a hyperbolic-elliptic coupled system on half space. J Partial Differ Equ. 2008;21:173–192.
  • Serre D. L1-stability of constants in a model for radiating gases. Commun Math Sci. 2003;1(1):197–205. doi: 10.4310/CMS.2003.v1.n1.a12
  • Wang W, Wang W, Wu Z. Decay of a model system of radiating gas. Math Methods Appl Sci. 2014;37(15):2331–2340. doi: 10.1002/mma.2984
  • Huang F, Li X. Convergence to the rarefaction wave for a model of radiating gas in one-dimension. Acta Math Sin Engl Ser. 2016;32(2):239–256. doi: 10.1007/s10255-016-0576-7
  • Liu H, Tadmor E. Critical thresholds in a convolution model for nonlinear conservation laws. SIAM J Math Anal. 2001;33(4):930–945. doi: 10.1137/S0036141001386908
  • Constantin A, Escher J. Wave breaking for nonlinear nonlocal shallow water equations. Acta Math. 1998;181(2):229–243. doi: 10.1007/BF02392586
  • Ma F, Liu Y, Qu C. Wave-breaking phenomena for the nonlocal Whitham-type equations. J Differ Equ. 2016;261(11):6029–6054. doi: 10.1016/j.jde.2016.08.027

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