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A quadratic interaction estimate for conservation laws: motivations, techniques and open problems

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Abstract

In a series of joint works with S. Bianchini [3, 4, 5], we proved a quadratic interaction estimate for general systems of conservation laws. Aim of this paper is to present the results obtained in the three cited articles [3, 4, 5], discussing how they are related with the general theory of hyperbolic conservation laws. To this purpose, first we explain why this quadratic estimate is interesting, then we give a brief overview of the techniques we used to prove it and finally we present some related open problems.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, 04109, Leipzig, Germany

    Stefano Modena

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  1. Stefano Modena
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Correspondence to Stefano Modena.

Additional information

This paper was written while the author was a Ph.D. student at Sissa, Trieste, Italy.

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Modena, S. A quadratic interaction estimate for conservation laws: motivations, techniques and open problems. Bull Braz Math Soc, New Series 47, 589–604 (2016). https://doi.org/10.1007/s00574-016-0171-9

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  • DOI: https://doi.org/10.1007/s00574-016-0171-9

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