General exact solutions in terms of wavelet expansion are obtained for multi- term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solv...General exact solutions in terms of wavelet expansion are obtained for multi- term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ- ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.展开更多
A closed form solution to the second order elasticity problem ,when an isotropiccompressible elastic half-space undergoes a deformation owing to a non-uniformlydistributed normal load,is presented,The method of integr...A closed form solution to the second order elasticity problem ,when an isotropiccompressible elastic half-space undergoes a deformation owing to a non-uniformlydistributed normal load,is presented,The method of integral transform is employedand the case when loading is distributed,in accordance with Hertz'x law ,is discussed.The limiting solution for incompressible isotropic elastic material is also derived.Numerical calculations for the second order elastic material for the displacement and the normal stress in the z-direction are carried out .It is found that,in comparison to the linear elastic case,the displacement increases and the normal stress decreases in the second order elastic material.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11032006,11072094,and 11121202)the Ph.D.Program Foundation of Ministry of Education of China(No.20100211110022)+2 种基金the National Key Project of Magneto-Constrained Fusion Energy Development Program(No.2013GB110002)the Fundamental Research Funds for the Central Universities(Nos.lzujbky-2012-202 and lzujbky-2013-1)the Scholarship Award for Excellent Doctoral Student Granted by Lanzhou University
文摘General exact solutions in terms of wavelet expansion are obtained for multi- term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ- ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.
文摘A closed form solution to the second order elasticity problem ,when an isotropiccompressible elastic half-space undergoes a deformation owing to a non-uniformlydistributed normal load,is presented,The method of integral transform is employedand the case when loading is distributed,in accordance with Hertz'x law ,is discussed.The limiting solution for incompressible isotropic elastic material is also derived.Numerical calculations for the second order elastic material for the displacement and the normal stress in the z-direction are carried out .It is found that,in comparison to the linear elastic case,the displacement increases and the normal stress decreases in the second order elastic material.
