Blow-up of the hyperbolic Burgers equation

Details Blow-up of the hyperbolic Burgers equation Blow-up of the hyperbolic Burgers equation

2007-04-27

arxiv.org/abs/0704.3710v1

Journal of Statistical Physics, Volume 127, Number 2 / April, 2007, 327-338

Physics

Mathematical Physics

Scientific paper

10.1007/s10955-006-9276-7

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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