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Blow-Up of the Hyperbolic Burgers Equation

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Abstract

The memory effects on microscopic kinetic systems have been sometimes modelled by means of the introduction of second order time derivatives in the macroscopic hydrodynamic equations. One prototypical example is the hyperbolic modification of the Burgers equation, that has been introduced to clarify the interplay of hyperbolicity and nonlinear hydrodynamic evolution. Previous studies suggested the finite time blow-up of this equation, and here we present a rigorous proof of this fact.

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  1. Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB, UK

    Carlos Escudero

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  1. Carlos Escudero
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Correspondence to Carlos Escudero.

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Escudero, C. Blow-Up of the Hyperbolic Burgers Equation. J Stat Phys 127, 327–338 (2007). https://doi.org/10.1007/s10955-006-9276-7

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  • DOI: https://doi.org/10.1007/s10955-006-9276-7

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