Asymptotic oscillations of solutions of scalar conservation laws with convexity under the action of a linear excitation

Author:
Athanasios N. Lyberopoulos

Journal:
Quart. Appl. Math. **48** (1990), 755-765

MSC:
Primary 35B40; Secondary 35B10, 35L65

DOI:
https://doi.org/10.1090/qam/1079918

MathSciNet review:
MR1079918

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References | Similar Articles | Additional Information

**[1]**C. M. Dafermos,*Characteristics in hyperbolic conservation laws. A study of the structure and the asymptotic behaviour of solutions*, Nonlinear analysis and mechanics: Heriot-Watt Symposium (Edinburgh, 1976), Vol. I, Pitman, London, 1977, pp. 1–58. Res. Notes in Math., No. 17. MR**0481581****[2]**C. M. Dafermos,*Generalized characteristics and the structure of solutions of hyperbolic conservation laws*, Indiana Univ. Math. J.**26**(1977), no. 6, 1097–1119. MR**0457947**, https://doi.org/10.1512/iumj.1977.26.26088**[3]**C. M. Dafermos,*Asymptotic behavior of solutions of hyperbolic balance laws*, Bifurcation phenomena in mathematical physics and related topics (Proc. NATO Advanced Study Inst., Cargèse, 1979) NATO Adv. Study Inst. Ser., Ser. C: Math. Phys. Sci., vol. 54, Reidel, Dordrecht-Boston, Mass., 1980, pp. 521–533. MR**580309****[4]**C. M. Dafermos,*Regularity and large time behaviour of solutions of a conservation law without convexity*, Proc. Roy. Soc. Edinburgh Sect. A**99**(1985), no. 3-4, 201–239. MR**785530**, https://doi.org/10.1017/S0308210500014256**[5]**C. M. Dafermos,*Hyperbolic systems of conservation laws*, Systems of nonlinear partial differential equations (Oxford, 1982) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 111, Reidel, Dordrecht, 1983, pp. 25–70. MR**725517****[6]**C. M. Dafermos,*Generalized characteristics in hyperbolic systems of conservation laws*, Arch. Rational Mech. Anal.**107**(1989), no. 2, 127–155. MR**996908**, https://doi.org/10.1007/BF00286497**[7]**Ronald J. DiPerna,*Decay and asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws*, Indiana Univ. Math. J.**24**(1974/75), no. 11, 1047–1071. MR**0410110**, https://doi.org/10.1512/iumj.1975.24.24088**[8]**A. F. Filippov,*Differential equations with discontinuous right-hand side*, Mat. Sb. (N.S.)**51 (93)**(1960), 99–128 (Russian). MR**0114016****[9]**J. M. Greenberg and Donald D. M. Tong,*Decay of periodic solutions of ∂𝑢/∂𝑡+∂𝑓(𝑢)/∂𝑥=0*, J. Math. Anal. Appl.**43**(1973), 56–71. MR**0320488**, https://doi.org/10.1016/0022-247X(73)90257-6**[10]**S. N. Kružkov,*First order quasilinear equations with several independent variables.*, Mat. Sb. (N.S.)**81 (123)**(1970), 228–255 (Russian). MR**0267257****[11]**P. D. Lax,*Hyperbolic systems of conservation laws. II*, Comm. Pure Appl. Math.**10**(1957), 537–566. MR**0093653**, https://doi.org/10.1002/cpa.3160100406**[12]**Tai Ping Liu,*Decay to 𝑁-waves of solutions of general systems of nonlinear hyperbolic conservation laws*, Comm. Pure Appl. Math.**30**(1977), no. 5, 586–611. MR**0450802**, https://doi.org/10.1002/cpa.3160300505**[13]**Athanasios Nikolaos Lyberopoulos,*Asymptotic oscillations of solutions of scalar conservation laws with or without convexity under the action of a linear excitation*, ProQuest LLC, Ann Arbor, MI, 1989. Thesis (Ph.D.)–Brown University. MR**2637669****[14]**A. I. Vol'pert,*The space BV and quasilinear equations*, Mat. Sbornik**73**(1967) (English translation: Math. USSR-Sbornik**2**, 225-267 (1967))

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DOI:
https://doi.org/10.1090/qam/1079918

Article copyright:
© Copyright 1990
American Mathematical Society