We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional sep...We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.展开更多
In this article a variable-domain variational approach to the entitled problem is presented.A pair of comple- mentary variational principles with a variable domain in terms of temperature and heat-streamfunction are f...In this article a variable-domain variational approach to the entitled problem is presented.A pair of comple- mentary variational principles with a variable domain in terms of temperature and heat-streamfunction are first established.Based on them,two methods of solution—generalized Ritz method and variable-domain FEM— both capable of handling problems with unknown boundaries,are suggested.Then,three sample numerical examples have been tested.The computational process is quite stable,and the results are encouraging.This variational approach can be extended straightforwardly to 3-D inverse problems as well as to other problems in mathematical physics.展开更多
By introducing an image plane, the inverse heat conduction problem with free boundary is transformed into one with completely known boundaryt which is much simpler to handle.As a by-product, the classical Kirchhoff’s...By introducing an image plane, the inverse heat conduction problem with free boundary is transformed into one with completely known boundaryt which is much simpler to handle.As a by-product, the classical Kirchhoff’s transformation for accounting for variable conductivity is rederived and an invariance property of the inverse problem solution with respect to variable conductivity is indicated. Then a pair of complementary extremum principles are established on the image plane, providing a sound theoretical foundation for the Ritz’s method and finite element method (FEM).An example solved by FEM is also given.展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.
文摘In this article a variable-domain variational approach to the entitled problem is presented.A pair of comple- mentary variational principles with a variable domain in terms of temperature and heat-streamfunction are first established.Based on them,two methods of solution—generalized Ritz method and variable-domain FEM— both capable of handling problems with unknown boundaries,are suggested.Then,three sample numerical examples have been tested.The computational process is quite stable,and the results are encouraging.This variational approach can be extended straightforwardly to 3-D inverse problems as well as to other problems in mathematical physics.
文摘By introducing an image plane, the inverse heat conduction problem with free boundary is transformed into one with completely known boundaryt which is much simpler to handle.As a by-product, the classical Kirchhoff’s transformation for accounting for variable conductivity is rederived and an invariance property of the inverse problem solution with respect to variable conductivity is indicated. Then a pair of complementary extremum principles are established on the image plane, providing a sound theoretical foundation for the Ritz’s method and finite element method (FEM).An example solved by FEM is also given.
