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Propagation properties for scalar conservation laws

Impacto



Díaz Díaz, Jesús Ildefonso y Kruzhkov, Stanislav Nicolayevich (1996) Propagation properties for scalar conservation laws. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique , 323 (5). pp. 463-468. ISSN 0764-4442

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Resumen

We study the propagation of an initial disturbance u(0)(x) of an equilibrium state s epsilon R for the scalar conservation law u(t) + phi(u)(x) = 0 in (0, + infinity) x R. We give a necessary and sufficient condition on phi for the following propagation property: if support of (u(0)(.) - s) is compact then the support of (u(0)(t,.) - s) is also compact for t epsilon [0, T-0), for some T-0 epsilon (0, + infinity]. The proofs are based on the study of suitable associated Riemann problems.


Tipo de documento:Artículo
Palabras clave:initial disturbance; Riemann problems
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:15836
Referencias:

Benilan Ph. and Kruzhkov S. N., 1994, 1995. Quasilinear Equations of the First Order with Continuous Nonlinearities, Doklady Rossiiskoi Akad. Nallk, 339. No. 2, pp. 151-154 (Eng1ish trans1ation in Russ. Acad. Sci. Doklady Matiz .(50, No. 3).

Diaz J. I. and Véron L., 1983. Existence theory and qualitative properties of the solutions of sorne first arder quaslilinear variational inequalities, Indiana Univ. Matiz. Journal, 32. No. 3. pp. 319-361.

Ge1fand 1. M., 1959. Sorne problerns in the theory of quasilinear equations. Uspekili Mat. Nauk. 17, No. 2, pp. 87-158.

Kersner R., Natalini R. and Tesei A., 1995. Shocks and free boundaries: the local behaviour, Asymptotic Allalysis. 10. Nº. 1. pp. 77-93.

Kruzhkov S. N., 1969. Generalized solutions of the Cauchy problerns in lhe 1arge far first order non-linear equations. Soviet Matil. Dokl., 10, No. 4, pp. 785-788.

Kruzhkov S. N. and Panov E. Yu., 1991. Conservative quasilinear first arder laws with an infinite dornain of dependence on initial data, Soviet Matil. Dokl.. 42, No. 2. pp. 316-321.

Kruzhkov S. N. and Petrosyan N. S., 1991. Asymptotic behaviour of lhe solutions of the Cauchy prob1ern for nonlinear first order equations, Russ. Math. Surveys, 42, No. 42, pp. 1-47.

Natalini R. and Tesei A., 1992. On a eJass of perturbed conservation 1aws, Advollces in Applied Motil., 13. pp. 429-453.

Rykov Y. G., 1986. On the behaviour of lhe supparts of genera1ized solutions of quasi-linear first arder equations far srnall and large values of time. Uspekili Mat. Nallk, 41. No. 4. p. 172.

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Última Modificación:06 Feb 2014 10:32

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