Geodesic
Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity
Applications of Mathematics, Tome 35 (1990) no. 3, pp. 184-191
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A parabolic system arisng as a viscosity regularization of the quasilinear one-dimensional telegraph equation is considered. The existence of $L \infty$ - a priori estimates, independent of viscosity, is shown. The results are achieved by means of generalized invariant regions.
A parabolic system arisng as a viscosity regularization of the quasilinear one-dimensional telegraph equation is considered. The existence of $L \infty$ - a priori estimates, independent of viscosity, is shown. The results are achieved by means of generalized invariant regions.
DOI : 10.21136/AM.1990.104402
Classification : 35B35, 35B45, 35B65, 35K45, 35K55, 73C50, 73D35, 74B20
Keywords: invariant region; vanishing viscosity; nonlinear parabolic system; quasilinear one- dimensional telegraph equation 
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Feireisl, Eduard. Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity. Applications of Mathematics, Tome 35 (1990) no. 3, pp. 184-191. doi: 10.21136/AM.1990.104402

[1] K. N. Chueh C. C. Conley J. A. Smoller: Positively invariant regions for systems of non linear diffusion equations. Indiana Univ. Math. J. 26 (1977), 372-7411. | MR

[2] C. M. Dafermos: Estimates for conservation laws with little viscosity. SIAM J. Math. Anal. 18 (1987), 409-421. | DOI | MR | Zbl

[3] R. J. DiPerna: Convergence of approximate solutions to conservation laws. Arch. Rational Mech. Anal. 82 (1983), 27-70. | DOI | MR | Zbl

[4] M. Rascle: Un résultat de ,,compacité par compensation à coefficients variables". Application à l'élasticité nonlinéaire. Compt. Rend. Acad. Sci. Paris, Série I, 302 (1986), 311 - 314. | MR

[5] D. Serre: Domaines invariants pour les systèmes hyperboliques de lois de conservation. J. Differential Equations 69 (1987), 46-62. | DOI | MR | Zbl

[6] D. Serre: La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations a une dimension d'espace. J. Math. pures et appl. 65 (1986), 423 - 468. | MR

[7] T. D. Venttseľ: Estimates of solutions of the one-dimensional system of equations of gas dynamics with "viscosity" nondepending on "viscosity". Soviet Math. J., 31 (1985), 3148- --3153. | DOI

[8] E. Feireisl: Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations. Apl. mat. 35 (1990), 192-208. | MR | Zbl

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