Blow-Up of the Hyperbolic Burgers Equation |
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Authors: | Carlos Escudero |
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Affiliation: | (1) Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB, UK |
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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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Keywords: | Fluid dynamics blow-up memory effects hyperbolicity |
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