On a nonlinear hyperbolic variational equation: II. The zero-viscosity and dispersion limits
On a nonlinear hyperbolic variational equation: II. The zero-viscosity and dispersion limits
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DOI：
10.1007/bf00379260
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发表时间：
1995-12
影响因子：
2.5
通讯作者：
J. K. Hunter;Yuxi Zheng
中科院分区：
文献类型：
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作者：
J. K. Hunter;Yuxi Zheng
我们用最简单的初始数据考虑非线性双曲型偏微分方程（ut+uux）x=1/2ux2的黏度和色散正则化，使得ux在有限时间内爆炸。证明了零黏度极限选择无黏度偏微分方程的唯一全局弱解。数值实验表明，零色散极限选择了相同初值问题的不同全局弱解。
We consider viscosity and dispersion regularizations of the nonlinear hyperbolic partial differential equation (ut+uux)x=1/2ux2with the simplest initial data such thatuxblows up in finite time. We prove that the zero-viscosity limit selects a unique global weak solution of the partial differential equation without viscosity. We also present numerical experiments which indicate that the zero-dispersion limit selects a different global weak solution of the same initial-value problem.