与参数识别问题相关的非经典等价变换
Nonclassical equivalence transformations associated with a parameter identification problem
摘要：
一类特殊的对称约化称为非经典等价变换讨论了一类参数识别问题所代表的偏微分方程。这些对称性约化涉及正问题和反问题，减少方程的维数，产生特殊类型的解，并且也可以被并入边界条件中。作为一个例子，我们讨论了非线性稳态热传导方程，并表明这种方法允许研究新类型的域上的模型。我们的MAPLE例程GENDEFNC使用包DESOLV（作者Carminati和Vu）已更新为这个建议，其输出是非经典等价变换的确定方程的非线性偏微分方程系统。
英文摘要：
A special class of symmetry reductions called nonclassical equivalence transformations is discussed in connection to a class of parameter identification problems represented by partial differential equations. These symmetry reductions relate the forward and inverse problems, reduce the dimension of the equation, yield special types of solutions, and may be incorporated into the boundary conditions as well. As an example, we discuss the nonlinear stationary heat conduction equation and show that this approach permits the study of the model on new types of domains. Our MAPLE routine GENDEFNC which uses the package DESOLV (authors Carminati and Vu) has been updated for this propose and its output is the nonlinear partial differential equation system of the determining equations of the nonclassical equivalence transformations.
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