Generalizations of the Greenberg-Rascle construction of periodic solutions to quasilinear equations of $1$-D elasticity
Author:
Robert Peszek
Journal:
Quart. Appl. Math. 57 (1999), 381-400
MSC:
Primary 35L70; Secondary 35B10, 35Q72, 74B20, 74H99
DOI:
https://doi.org/10.1090/qam/1686196
MathSciNet review:
MR1686196
Full-text PDF Free Access
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Additional Information
- J. M. Greenberg and M. Rascle, Time-periodic solutions to systems of conservation laws, Arch. Rational Mech. Anal. 115 (1991), no. 4, 395–407. MR 1120854, DOI https://doi.org/10.1007/BF00375281
- J. M. Greenberg and Robert Peszek, Time-periodic solutions to a class of quasilinear wave equations, Arch. Rational Mech. Anal. 122 (1993), no. 1, 35–51. MR 1207240, DOI https://doi.org/10.1007/BF01816554
- R. J. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82 (1983), no. 1, 27–70. MR 684413, DOI https://doi.org/10.1007/BF00251724
- Denis Serre, La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations à une dimension d’espace, J. Math. Pures Appl. (9) 65 (1986), no. 4, 423–468 (French). MR 881690
- Peter D. Lax, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Mathematical Phys. 5 (1964), 611–613. MR 165243, DOI https://doi.org/10.1063/1.1704154
- R. C. MacCamy and V. J. Mizel, Existence and nonexistence in the large of solutions of quasilinear wave equations, Arch. Rational Mech. Anal. 25 (1967), 299–320. MR 216165, DOI https://doi.org/10.1007/BF00250932
J. Greenberg and M. Rascle, Time periodic solutions of conservation laws, Arch. Rational Mech. Anal. 115, 395–407 (1991)
J. Greenberg and R. Peszek, Time periodic solutions to a class of quasi-linear wave equations, Arch. Rational Mech. Anal. 122, 35–51 (1993)
R. J. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82, 27–70 (1983)
D. Serre, La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations à une dimension d’espace, J. Math. Pures Appl. (9) 65, 423–468 (1986)
P. Lax, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys. 5, 611–613 (1964)
R. C. MacCamy and V. J. Mizel, Existence and nonexistence in the large of solutions of quasilinear wave equations, Arch. Rational Mech. Anal. 25, 299–320 (1967)
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Article copyright:
© Copyright 1999
American Mathematical Society