Stochastic analysis method for hopf's equation ut+ uux=0
作者:
Cheng Shaozhong,
期刊:
Stochastic Analysis and Applications
(Taylor Available online 1997)
卷期:
Volume 15,
issue 3
页码: 419-430
ISSN:0736-2994
年代: 1997
DOI:10.1080/07362999708809485
出版商: Marcel Dekker, Inc.
关键词: Stochastic Partial Differential Equation;Quasi-Linear Partial Differential Equation;Stochastic Characteristic;Viscosity Method;Entropy condition
数据来源: Taylor
摘要:
It is proved that the stochastic charactcrtstics of Burgers’ equation ut+uux=μuxxconverge in probability to the character is tcs of Hopf ’ s cqua lion ut+uux=0 as the viscosity μ →0. It follows naturally that the solution of Burgers’ equation converges to the solution of Hopf 's equation satisfying entropy condition. This is well known result due to E. Hopf in 1950. The method here is new. This paper suggests that this method may be useful for proving the validity of “vanishing viscosity method” in certain cases. Those problems are usually extremely difficult.
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