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*, Nonlinear Analysis and Mechanics (R.J. Knops, Ed.), Research Notes in Math. No. 17, Pitman, London, 1977, pp. 1-58 MR**0481581****[2]**C. M. Dafermos,*Generalized characteristics and the structure of solutions of hyperbolic conservation laws*, Indiana Univ. Math. J.**26**, 1097-1119 (1977) MR**0457947****[3]**C. M. Dafermos,*Asymptotic behavior of solutions of hyperbolic balance laws*, Bifurcation Phenomena in Mathematical Physics (C. Bardos and D. Bessis, Eds.), D. Reidel, Dordrecht, 1979, pp. 521-533 MR**580309****[4]**C. M. Dafermos,*Regularity and large time behavior of solutions of a conservation law without convexity*, Proc. Roy. Soc. Edinburgh**99A**, 201-239 (1985) MR**785530****[5]**C. M. Dafermos,*Hyperbolic systems of conservation laws*, Systems of Nonlinear Partial Differential Equations (J.M. Ball, Ed.), NATO ASI Series C No. 111, D. 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**, 127-155 (1989) MR**996908****[7]**R. J. Diperna,*Decay and asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws*, Indiana Univ. Math. J.**24**, 1047-1071 (1975) MR**0410110****[8]**A. F. Filippov,*Differential equations with discontinuous right-hand side*, Mat. Sbornik (N.S.)**51**, 99-128 (1960) (English translation: Amer. Math. Soc. Transl. Ser. 2**42**, 199-231 (1964)) MR**0114016****[9]**J. M. Greenberg and D. D. Tong,*Decay of periodic solutions of*, J. Math. Anal. Appl.**43**, 56-71 (1973) MR**0320488****[10]**S. N. Kružkov,*First order quasilinear equations in several independent variables*, Mat. Sbornik (N.S.)**81**, 228-255 (1970) (English translation: Math. USSR-Sbornik**10**, 217-243 (1970)) MR**0267257****[11]**P. D. Lax,*Hyperbolic systems of conservation laws II*, Comm. Pure Appl. Math.**10**, 537-566 (1957) MR**0093653****[12]**T.-P. Liu,*Decay to N-waves of solutions of general systems of nonlinear hyperbolic conservation laws*, Comm. Pure Appl. Math.**30**, 585-610 (1977) MR**0450802****[13]**A. N. Lyberopoulos,*Asymptotic oscillations of solutions of scalar conservation laws with or without convexity under the action of a linear excitation*, Ph.D. dissertation, Brown University, 1989 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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Additional Information

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

Article copyright:
© Copyright 1990
American Mathematical Society