标题： 双曲 Burgers 方程的爆破 显示英文标题

标题： Blow-up of the hyperbolic Burgers equation

摘要： 微观动力学系统中的记忆效应有时通过在宏观流体力学方程中引入二阶时间导数来建模。 一个典型的例子是Burgers方程的双曲修正形式，该形式被引入以阐明双曲性和非线性流体力学演化的相互作用。 先前的研究表明了该方程有限时间爆破的现象，本文给出了这一事实的严格证明。 显示英文摘要

摘要： 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.