Well Posedness of Balance Laws with Non-Characteristic Boundary
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 875-894.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

This note presents a well posedness result for the initial-boundary value problem consisting of a nonlinear system of hyperbolic balance laws with boundary, in the non-characteristic case.
Questa nota presenta un risultato di buona positura per un problema ai valori iniziali ed al contorno per un sistema non lineare di leggi di bilancio, nel caso non caratteristico.
@article{BUMI_2007_8_10B_3_a29,
     author = {Colombo, Rinaldo M. and Rosini, Massimiliano D.},
     title = {Well {Posedness} of {Balance} {Laws} with {Non-Characteristic} {Boundary}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {875--894},
     publisher = {mathdoc},
     volume = {Ser. 8, 10B},
     number = {3},
     year = {2007},
     zbl = {1180.35341},
     mrnumber = {2507903},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a29/}
}
TY  - JOUR
AU  - Colombo, Rinaldo M.
AU  - Rosini, Massimiliano D.
TI  - Well Posedness of Balance Laws with Non-Characteristic Boundary
JO  - Bollettino della Unione matematica italiana
PY  - 2007
SP  - 875
EP  - 894
VL  - 10B
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a29/
LA  - en
ID  - BUMI_2007_8_10B_3_a29
ER  - 
%0 Journal Article
%A Colombo, Rinaldo M.
%A Rosini, Massimiliano D.
%T Well Posedness of Balance Laws with Non-Characteristic Boundary
%J Bollettino della Unione matematica italiana
%D 2007
%P 875-894
%V 10B
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a29/
%G en
%F BUMI_2007_8_10B_3_a29
Colombo, Rinaldo M.; Rosini, Massimiliano D. Well Posedness of Balance Laws with Non-Characteristic Boundary. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 875-894. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a29/

[1] F. Ancona - G. M. Coclite, On the attainable set for Temple class systems with boundary controls, SIAM J. Control Optim, 43 (6) (electronic, 2005), 2166-2190. | DOI | MR | Zbl

[2] D. Amadori - R. M. Colombo, Continuous dependence for 2x2 conservation laws with boundary, J. Differential Equations, 138 (2) (1997), 229-266. | DOI | MR | Zbl

[3] D. Amadori - G. Guerra, Global weak solutions for systems of balance laws, Appl. Math. Lett., 12 (6) (1999), 123-127. | DOI | MR | Zbl

[4] P. Baiti - A. Bressan, The semigroup generated by a Temple class system with large data, Differential Integral Equations, 10 (3) (1997), 401-418. | MR | Zbl

[5] S. Bianchini, The semigroup generated by a Temple class system with non-convex flux function, Diff. Integral Equations, 13 (10-12) (2000), 1529-1550. | MR | Zbl

[6] A. Bressan, Hyperbolic systems of conservation laws, volume 20 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford, 2000. The one-dimensional Cauchy problem. | MR

[7] A. Bressan - R. M. Colombo, The semigroup generated by 2x2 conservation laws, Arch. Rational Mech. Anal., 133 (1) (1995), 1-75. | DOI | MR | Zbl

[8] R. M. Colombo, Wave front tracking in systems of conservation laws, Appl. Math., 49 (6) (2004), 501-537. | fulltext EuDML | DOI | MR | Zbl

[9] R. M. Colombo - A. Corli, On a class of hyperbolic balance laws, J. Hyperbolic Differ. Equ., 1 (4) (2004), 725-745. | DOI | MR | Zbl

[10] R. M. Colombo - A. Groli, On the initial boundary value problem for Temple systems, Nonlinear Anal., 56 (4) (2004), 569-589. | DOI | MR | Zbl

[11] R. M. Colombo - N. H. Risebro, Continuous dependence in the large for some equations of gas dynamics, Comm. Partial Differential Equations, 23 (9-10) (1998), 1693-1718. | DOI | MR

[12] R. M. Colombo - M. D. Rosini, Well posedness of balance laws with boundary, J. Math. Anal. Appl., 311 (2) (2005), 683-702. | DOI | MR | Zbl

[13] G. Crasta - B. Piccoli, Viscosity solutions and uniqueness for systems of inhomo- geneous balance laws, Discrete Contin. Dynam. Systems, 3 (4) (1997), 477-502. | DOI | MR | Zbl

[14] C. M. Dafermos, Hyperbolic conservation laws in continuum physics, volume 325 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 2000. | DOI | MR | Zbl

[15] C. M. Dafermos - L. Hsiao, Hyperbolic systems and balance laws with inhomo- geneity and dissipation, Indiana Univ. Math. J., 31 (4) (1982), 471-491. | DOI | MR | Zbl

[16] C. Donadello - A. Marson, Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws, No.D.E.A., to appear. | DOI | MR | Zbl

[17] A. F. Filippov, Differential equations with discontinuous righthand sides, Kluwer Academic Publishers Group, Dordrecht, 1988. | DOI | MR

[18] J. Goodman, Initial Boundary Value Problems for Hyperbolic Systems of Conservation Laws, PhD thesis, California University, 1982.

[19] D. Hoff, Invariant regions for systems of conservation laws, Trans. Amer. Math. Soc., 289 (2) (1985), 591-610. | DOI | MR | Zbl

[20] T. P. Liu, Quasilinear hyperbolic systems, Comm. Math. Phys., 68 (2) (1979), 141- 172. | MR | Zbl

[21] M. Nagumo, Über die Lage der Integralkurven gewoÈhnlicher Differentialgleichungen, Proc. Phys.-Math. Soc. Japan (3), 24 (1942), 551-559. | MR | Zbl

[22] D. Serre, Solutions à variations bornées pour certains systèmes hyperboliques de lois de conservation, J. Differential Equations, 68 (2) (1987), 137-168. | DOI | MR | Zbl