¹University of Science and Technology of China, Department of Mathematics, Hefei 230026, China.
E-mail: mtao@mail.ustc.edu.cn
²University of Science and Technology of China, Department of Mathematics, Hefei 230026, China.
E-mail: czx@mail.ustc.edu.cn
³University of Science and Technology of China, Department of Mathematics, Hefei 230026, China.
E-mail: yanjin@mail.ustc.edu.cn

In this paper, we apply the maximum principle and the compensated compactness method to get the existence of weak solutions to the Cauchy problems for the nonlinear hyperbolic conservation laws of quadratic flux and the LeRoux system with sources.

Key words: Weak solution, maximum principle, entropy-entropy flux pair, compensated compactness, Dirac measure.

En este artículo aplicamos el principio del máximo y el método de la compactificación compensada para obtener soluciones débiles a los problemas de Cauchy para las leyes de conservación hiperbólica, no lineal, de flujo cuadrático y el sistema LeRoux con fuentes..

Palabras clave: Soluciones débiles, principio del máximo, flujo par entropía−entropía, compactificación compensada, medida de Dirac.

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