The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so t...The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.展开更多
In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain of QT with stro...In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain of QT with strong restrictions to the measured boundary data. On the other hand, weakening the conditions on the measured data, then combining the duality method in optimization with the quasi-reversibility method, we solve the Cauchy problems for parabolic equations in the presence of noisy data. Using this method, we can get the proper regularization parameter ε that we need in the quasi-reversibility method and obtain the convergence rate of approximate solutions as the noise of amplitude δ tends to zero.展开更多
In this paper,a Cauchy problem of two-dimensional heat conduction equation is investigated.This is a severely iⅡ-posed problem.Based on the solution of Cauchy problem of two-dimensional heat conduction equation,we pr...In this paper,a Cauchy problem of two-dimensional heat conduction equation is investigated.This is a severely iⅡ-posed problem.Based on the solution of Cauchy problem of two-dimensional heat conduction equation,we propose to solve this problem by modifying the kernel,which generates a well-posed problem.Error estimates between the exact solution and the regularized solution are given.We provide a numerical experiment to illustrate the main results.展开更多
文摘The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.
基金supported by National Natural Science Foundation of China (Grant No.11226166)Scientific Research Fund of Hu'nan Provincial Education Department (Grant No.11C0052)
文摘In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain of QT with strong restrictions to the measured boundary data. On the other hand, weakening the conditions on the measured data, then combining the duality method in optimization with the quasi-reversibility method, we solve the Cauchy problems for parabolic equations in the presence of noisy data. Using this method, we can get the proper regularization parameter ε that we need in the quasi-reversibility method and obtain the convergence rate of approximate solutions as the noise of amplitude δ tends to zero.
基金supported by the National Natural Science Foundation of China(11101109,11271102)and the Natural Science Foundation of Heilongjiang Province of China(A201107).
文摘In this paper,a Cauchy problem of two-dimensional heat conduction equation is investigated.This is a severely iⅡ-posed problem.Based on the solution of Cauchy problem of two-dimensional heat conduction equation,we propose to solve this problem by modifying the kernel,which generates a well-posed problem.Error estimates between the exact solution and the regularized solution are given.We provide a numerical experiment to illustrate the main results.
