Título inglés |
Fundamental solutions and singular shocks in scalar conservation laws. |
Título español |
Soluciones fundamentales y shocks singulares en leyes de conservación escalares. |
Autor/es |
Chasseigne, Emmanuel |
Organización |
Lab. Math. Univ. Tours, Tours, Francia |
Revista |
1139-1138 |
Publicación |
2003, 16 (2): 443-463, 15 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
We study the existence and non-existence of fundamental solutions for the scalar conservation laws ut + f(u)x = 0, related to convexity assumptions on f. We also study the limits of those solutions as the initial mass goes to infinity. We especially prove the existence of so-called Friendly Giants and Infinite Shock Solutions according to the convexity of f, which generalize the explicit power case f(u) = um. We introduce an extended notion of solution and entropy criterion to allow infinite shocks in the theory, and the initial data also has to be understood in a generalized sense, since locally infinite measures appear. |
Clasificación UNESCO |
120220 |
Palabras clave español |
Ecuaciones diferenciales hiperbólicas ; Teorema de existencia ; Solución débil ; Singularidades ; Discontinuidad ; Funciones convexas |
Código MathReviews |
MR2032927 |
Código Z-Math |
Zbl 1057.35002 |
Acceso al artículo completo |