# Viscosity solutions and standard Riemann semigroup for conservation laws with boundary

Debora Amadori; Rinaldo M. Colombo

Rendiconti del Seminario Matematico della Università di Padova (1998)

- Volume: 99, page 219-245
- ISSN: 0041-8994

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topAmadori, Debora, and Colombo, Rinaldo M.. "Viscosity solutions and standard Riemann semigroup for conservation laws with boundary." Rendiconti del Seminario Matematico della Università di Padova 99 (1998): 219-245. <http://eudml.org/doc/108474>.

@article{Amadori1998,

author = {Amadori, Debora, Colombo, Rinaldo M.},

journal = {Rendiconti del Seminario Matematico della Università di Padova},

keywords = {characteristic and noncharacteristic formulation; viscosity solution with small total variation},

language = {eng},

pages = {219-245},

publisher = {Seminario Matematico of the University of Padua},

title = {Viscosity solutions and standard Riemann semigroup for conservation laws with boundary},

url = {http://eudml.org/doc/108474},

volume = {99},

year = {1998},

}

TY - JOUR

AU - Amadori, Debora

AU - Colombo, Rinaldo M.

TI - Viscosity solutions and standard Riemann semigroup for conservation laws with boundary

JO - Rendiconti del Seminario Matematico della Università di Padova

PY - 1998

PB - Seminario Matematico of the University of Padua

VL - 99

SP - 219

EP - 245

LA - eng

KW - characteristic and noncharacteristic formulation; viscosity solution with small total variation

UR - http://eudml.org/doc/108474

ER -

## References

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- [2] D. Amadori - R. M. COLOMBO, Continuous dependence for 2 x 2 conservation laws with boundary, J. Differential Equations, 138 (1997), no. 2, pp. 229-266. Zbl0884.35091MR1462268
- [3] A. Bressan, Global solutions of systems of conservation laws by wave-front tracking, J. Math. Anal. Appl., 170 (1992), pp. 414-432. Zbl0779.35067MR1188562
- [4] A. Bressan, Lecture notes on systems of conservation laws, S.I.S.S.A., Trieste (1994).
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- [7] A. Bressan - R.M. Colombo, The semigroup generated by 2 x 2 systems of conservation laws, Arch. Rational Mech. Anal., 133 (1996), pp. 1-75. Zbl0849.35068MR1367356
- [8] A. Bressan - R.M. Colombo, Unique solutions of 2 x 2 conservation laws with large data, Indiana Univ. Math. J., 44 (1995), pp. 677-725. Zbl0852.35092MR1375345
- [9] A. Bressan - G. Crasta - B. Piccoli, Well-posedness of the Cauchy problem for n x n systems of conservation laws, Preprint S.I.S.S.A. 1996. Zbl0958.35001
- [10] R.M. Colombo, Uniqueness and continuous dependence for 2 × 2 conservation laws, Ph.D. Thesis, S.I.S.S.A. (1995).
- [11] F. Dubois - P. Le Floch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differential Equations, 71 (1988), pp. 93-122. Zbl0649.35057MR922200
- [12] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18 (1965), pp. 697-715. Zbl0141.28902MR194770
- [13] J. Goodman, Initial Boundary Value Problems for Hyperbolic Systems of Conservation Laws, Ph. D. Thesis, California University (1982).
- [14] P. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., 10 (1957), pp. 537-567. Zbl0081.08803MR93653
- [15] M. Sablé-Tougeron, Méthode de Glimm et problème mixte, Ann. Inst. Henri Poincaré, 10, no. 4 (1993), pp. 423-443. Zbl0832.35093MR1246461
- [16] J. Smoller, Shock Waves and Reaction-DiffusionEquations, Springer-Verlag, New York (1983). Zbl0807.35002MR688146

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