Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types
Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types
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DOI：
10.1215/s0012-7094-04-12722-8
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发表时间：
2005-04
影响因子：
2.5
通讯作者：
D. Lupo;K. Payne
中科院分区：
文献类型：
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作者：
D. Lupo;K. Payne
对于混合椭圆双曲和退化类型的偏微分方程，这是欧拉-拉格朗日方程的一个相关的拉格朗日量，不变性相对于独立和因变量的变化进行了研究，是在连续的单参数对称群的分类结果。对于变分和发散对称性，通过乘子法导出守恒律。由各向异性膨胀产生的守恒律被用来证明线性和非线性问题的唯一性定理，线性部分的膨胀下的不变性被用来导出临界指数现象，并获得超临界问题的局部化能量估计。
For partial differential equations of mixed elliptic-hyperbolic and degenerate types which are the Euler-Lagrange equations for an associated Lagrangian, invariance with respect to changes in independent and dependent variables is investigated, as are results in the classification of continuous one-parameter symmetry groups. For the variational and divergence symmetries, conservation laws are derived via the method of multipliers. The conservation laws resulting from anisotropic dilations are applied to prove uniqueness theorems for linear and nonlinear problems, and the invariance under dilations of the linear part is used to derive critical exponent phenomena and to obtain localized energy estimates for supercritical problems.