Fundamental solutions and singular shocks in scalar conservation laws

• Autores: Emmanuel Chasseigne
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 16, Nº 2, 2003, págs. 443-463
• Idioma: inglés
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• Resumen

  • 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.