[1] Anderson, J.D.: Hypersonic and High Temperature Gas Dynamics. AIAA Education Series, 2nd edn. McGraw-Hill (2006) [2] Bouchut, F.: On zero pressure gas dynamics. In: Perthame, B. (ed) Advances in Kinetic Theory and Computing. Ser. Adv. Math. Appl. Sci., vol. 22, pp. 171–190. World Sci. Publ., River Edge, NJ (1994) [3] Bouchut, F., James, F.: One-dimensional transport equations with discontinuous coefficients. Nonlinear Anal. 32(7), 891–933 (1998) [4] Brenier, Y.: Solutions with concentration to the Riemann problem for the one-dimensional Chaplygin gas equations. J. Math. Fluid Mech. 7(suppl.3), S326–S331 (2005) [5] Bressan, A.: Hyperbolic systems of conservation laws. The one-dimensional Cauchy problem. Oxford Lecture Series in Mathematics and Its Applications, vol. 20. Oxford University Press, Oxford (2000) [6] Bressan, A.: Open questions in the theory of one dimensional hyperbolic conservation laws. In: Nonlinear Conservation Laws and Applications, IMA Vol. Math. Appl., vol. 153, pp. 1–22. Springer, New York (2011) [7] Chang, T., Hsiao, L.: The Riemann problem and interaction of waves in gas dynamics. Pitman Monographs and Surveys in Pure and Applied Mathematics, 41. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York (1989) [8] Chang, T., Tan, D.: Two-dimensional Riemann problem for a hyperbolic system of conservation laws. Acta Math. Sci. (English Ed.) 11(4), 369–392 (1991) [9] Chen, G.-Q., Liu, H.: Formation of δ-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids. SIAM J. Math. Anal. 34(4), 925–938 (2003) [10] Cheng, S., Li, J., Zhang, T.: Explicit construction of measure solutions of Cauchy problem for transportation equations. Sci. China Ser. A 40(12), 1287–1299 (1997) [11] Colombeau, J.F.: Multiplication of Distributions: A tool in Mathematics, Numerical Engineering and Theoretical Physics. Lecture Notes in Mathematics, vol. 1532. Springer-Verlag, Berlin (1992) [12] Dafermos, C.M.: Hyperbolic Conservation Laws in Continuum Physics. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 325, 3rd edn. Springer-Verlag, Berlin (2010) [13] Daw, D., Nedeljkov, M.: Shadow waves for pressureless gas balance laws. Appl. Math. Lett. 57, 54–59 (2016) [14] E, W., Rykov, Y.G., Sinai, Y.G.: Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics. Commun. Math. Phys. 177(2), 349–380 (1996) [15] Gao, L., Qu, A., Yuan, H.: Delta shock as free piston in pressureless Euler flows. Preprint (2021) [16] Guerra, G., Shen, W.: Vanishing viscosity and backward Euler approximations for conservation laws with discontinuous flux. SIAM J. Math. Anal. 51(4), 3112–3144 (2019) [17] Guo, L., Sheng, W., Zhang, T.: The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system. Commun. Pure Appl. Anal. 9(2), 431–458 (2010) [18] Holden, H., Risebro, N.H.: Front tracking for hyperbolic conservation laws. In: Antman, S.S., Marsden, J.E., Sirovich, L. (eds) Applied Mathematical Sciences, vol. 152, 2nd edn. Springer, Heidelberg (2015) [19] Hu, D.: The supersonic flow past a wedge with large curved boundary. J. Math. Anal. Appl. 462(1), 380–389 (2018) [20] Huang, F., Wang, Z.: Well posedness for pressureless flow. Commun. Math. Phys. 222(1), 117–146 (2001) [21] Jiang, W., Li, T., Wang, Z., Fang, S.: The limiting behavior of the Riemann solutions of non-isentropic modified Chaplygin gas dynamics. J. Math. Phys. 62(4), 041501 (2021) [22] Jin, Y., Qu, A., Yuan, H.: On two-dimensional steady hypersonic-limit Euler flows passing ramps and Radon measure solutions of compressible Euler equations. Commun. Math. Sci., to apear (2019). arXiv:1909.03624v1 [23] Jin, Y., Qu, A., Yuan, H.: Radon measure solutions for steady compressible hypersonic-limit Euler flows passing cylindrically symmetric conical bodies. Commun. Pure Appl. Anal. 20(7/8), 2665–2685 (2021) [24] Keyfitz, B.L.: Conservation laws, delta-shocks and singular shocks. In: Nonlinear Theory of Generalized Functions (Vienna, 1997), Chapman & Hall/CRC Res. Notes Math., vol. 401. pp. 99–111, Chapman & Hall/CRC, Boca Raton, FL (1999) [25] Korchinski, D.J.: Solution of a Riemann Problem for a 2×2 System of Conservation Laws Possessing no Classical Weak Solution. Thesis (Ph.D.). Adelphi University. ProQuest LLC, Ann Arbor, MI (1977) [26] LeFloch, P.G.: An existence and uniqueness result for two nonstrictly hyperbolic systems. In: Nonlinear Evolution Equations that Change Type. IMA Vol. Math. Appl. vol. 27, pp. 126–138. Springer, New York (1990) [27] LeFloch, P.G., Thanh, M.D.: The Riemann problem for the shallow water equations with discontinuous topography. Commun. Math. Sci. 5(4), 865–885 (2007) [28] Li, J.: Note on the compressible Euler equations with zero temperature. Appl. Math. Lett. 14(4), 519–523 (2001) [29] Li, J., Warnecke, G.: Generalized characteristics and the uniqueness of entropy solutions to zero-pressure gas dynamics. Adv. Differ. Equ. 8(8), 961–1004 (2003) [30] Li, J., Zhang, T., Yang, S.: The Two-Dimensional Riemann Problem in Gas Dynamics. Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 98. Longman, Harlow (1998) [31] Nedeljkov, M.: Unbounded solutions to some systems of conservation laws—split delta shock waves. In: Proceedings of the 5th International Symposium on Mathematical Analysis and Its Applications (Niška Banja, 2002) Mat. Vesnik 54(3/4), 145–149 (2002) [32] Nedeljkov, M.: Delta and singular delta locus for one-dimensional systems of conservation laws. Math. Methods Appl. Sci. 27(8), 931–955 (2004) [33] Nedeljkov, M., Oberguggenberger, M.: Interactions of delta shock waves in a strictly hyperbolic system of conservation laws. J. Math. Anal. Appl. 344(2), 1143–1157 (2008) [34] Neumann, L., Oberguggenberger, M., Sahoo, M. R., Sen, A.: Initial-boundary value problem for 1D pressureless gas dynamics (2021). https://arxiv.org/abs/2104.10537v1 [35] Paiva, A.: Formation of δ-shock waves in isentropic fluids. Z. Angew. Math. Phys. 71(4), 110, 12 (2020) [36] Qu, A., Yuan, H.: Measure solutions of one-dimensional piston problem for compressible Euler equations of Chaplygin gas. J. Math. Anal. Appl. 481(1), 123486 (2020). (10) [37] Qu, A., Yuan, H.: Radon measure solutions for steady compressible Euler equations of hypersonic-limit conical flows and Newton’s sine-squared law. J. Differ. Equ. 269(1), 495–522 (2020) [38] Qu, A., Yuan, H., Zhao, Q.: High Mach number limit of one-dimensional piston problem for non-isentropic compressible Euler equations: polytropic gas. J. Math. Phys. 61(1), 011507 (2020) [39] Qu, A., Yuan, H., Zhao, Q.: Hypersonic limit of two-dimensional steady compressible Euler flows passing a straight wedge. ZAMM Z. Angew. Math. Mech. 100(3), e201800225 (2020) [40] Riemann, B.: The propagation of planar air waves of finite amplitude. Abh. Ges. Wiss. Göttingen 8, 43–65 (1860) [41] Schwartz, L.: Théorie des distributions. (French) Nouvelle édition, entiérement corrigée, refondue et augmentée. Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X Hermann, Paris (1966) [42] Shen, C., Sun, M., Wang, Z.: Global structure of Riemann solutions to a system of two-dimensional hyperbolic conservation laws. Nonlinear Anal. Theory Methods Appl. 74(14), 4754–4770 (2011) [43] Sheng, W., Zhang, T.: The Riemann problem for the transportation equations in gas dynamics. Mem. Am. Math. Soc. 137(654), viii+77 (1999) [44] Smoller, J.: Shock Waves and Reaction-Diffusion Equations. Springer-Verlag, New York (1994) [45] Tan, D., Zhang, T.: Two-dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws. I. Four-J cases. J. Differ. Equ. 111(2), 203–254 (1994) [46] Tan, D., Zhang, T., Zheng, Y.: Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws. J. Differ. Equ. 112(1), 1–32 (1994) [47] Wang, Z., Huang, F., Ding, X.: On the Cauchy problem of transportation equations. Acta Math. Appl. Sinica (English Ser.) 13(2), 113–122 (1997) [48] Yang, H., Zhang, Y.: New developments of delta shock waves and its applications in systems of conservation laws. J. Differ. Equ. 252(11), 5951–5993 (2012) |