Existencia de una solución débil entrópica para un sistema de tipo Keyfitz-Kranzer simétrico

Existence of Weak Entropy Solution for a Symmetric System of Keyfitz-Kranzer Type

Consideramos el problema de Cauchy para un sistema 2\times2 de tipo Keyfitz-Kranzer simétrico con valor inicial acotado y medible. La existencia de una solución débil entrópica para este sistema es probada mediante el uso de viscosidad clásica, una L¹(R) estimativa relacionada con uno de los invariantes de Riemann y el lema del divergente-rotacional, pero evitando el uso de medidas de Young.

We consider the Cauchy problem for a 2\times2 symmetric system of Keyfitz-Kranzer type with bounded measurable initial data. The existence of a weak entropy solution to this system is proved by using classical viscosity, an estimate in L¹(R) related to one of the Riemann invariants and the div-curl lemma, but avoiding the use of Young measures.

Existence of Weak Entropy Solution for a Symmetric System of Keyfitz-Kranzer Type Existencia de una solución débil entrópica para un sistema de tipo Keyfitz-Kranzer simétrico JUAN CARLOS HERNÁNDEZ R.¹

¹Universidad Nacional de Colombia, Bogotá, Colombia. Email: jchernandezri@unal.edu.co

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Abstract

We consider the Cauchy problem for a 2\times2 symmetric system of Keyfitz-Kranzer type with bounded measurable initial data. The existence of a weak entropy solution to this system is proved by using classical viscosity, an estimate in L¹(R) related to one of the Riemann invariants and the div-curl lemma, but avoiding the use of Young measures.

Key words: System of Keyfitz-Kranzer type, Existence, Weak entropy solution.

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2000 Mathematics Subject Classification: 35D05, 35L65.

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Resumen

Consideramos el problema de Cauchy para un sistema 2\times2 de tipo Keyfitz-Kranzer simétrico con valor inicial acotado y medible. La existencia de una solución débil entrópica para este sistema es probada mediante el uso de viscosidad clásica, una L¹(R) estimativa relacionada con uno de los invariantes de Riemann y el lema del divergente-rotacional, pero evitando el uso de medidas de Young.

Palabras clave: Sistema de tipo Keyfitz-Kranzer, existencia, solución débil entrópica.

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References

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(Recibido en enero de 2012. Aceptado en mayo de 2013)

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv47n1a02,
    AUTHOR  = {Hernández R., Juan Carlos},
    TITLE   = {{Existence of Weak Entropy Solution for a Symmetric System of Keyfitz-Kranzer Type}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2013},
    volume  = {47},
    number  = {1},
    pages   = {13--28}
}

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