By combining the wavelet decomposition with kernel method, a practical approach of universal multi-scale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identification schem...By combining the wavelet decomposition with kernel method, a practical approach of universal multi-scale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identification scheme using wavelet support vector machines (WSVM) estimator is proposed for nonlinear dynamic systems. The good approximating properties of wavelet kernel function enhance the generalization ability of the proposed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.展开更多
We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space...We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space yC^1,W^2,2（[0,T）,R^n）,n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space yC^1,L^2（[0,T）,R^n）,n≤ 3.展开更多
基金the National 973 Key Fundamental Research Project of China (Grant No.2002CB312200)
文摘By combining the wavelet decomposition with kernel method, a practical approach of universal multi-scale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identification scheme using wavelet support vector machines (WSVM) estimator is proposed for nonlinear dynamic systems. The good approximating properties of wavelet kernel function enhance the generalization ability of the proposed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.
基金Supported by Ministry of Science of Republic Serbia
文摘We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space yC^1,W^2,2（[0,T）,R^n）,n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space yC^1,L^2（[0,T）,R^n）,n≤ 3.
