This paper is concerned with the stationary plane contact of an insulated rigid punch and a half-space which is elastically anisotropic but thermally conducting. The frictional heat generation inside the contact regio...This paper is concerned with the stationary plane contact of an insulated rigid punch and a half-space which is elastically anisotropic but thermally conducting. The frictional heat generation inside the contact region due to the sliding of the punch over the half-space surface and the heat radiation outside the contact region are taken into account. With the help of Fourier integral transform, the problem is reduced to a system of two singular integral equations. The equations are solved numerically by using Gauss-Jacobi and trapezoidal-rule quadratures. The effects of anisotropy and thermal effects are shown graphically.展开更多
In this paper we consider a non-standard inverse heat conduction problem for determining surface heat flux from an interior observation which appears in some applied subjects. This problem is ill-posed in the sense th...In this paper we consider a non-standard inverse heat conduction problem for determining surface heat flux from an interior observation which appears in some applied subjects. This problem is ill-posed in the sense that the solution (if it exists)does not depend continuously on the data. A Fourier method is applied to formulate a regularized approximation solution, and some sharp error estimates are also given.展开更多
In this paper we apply the Fourier transform to prove the Hyers-Ulam-Rassias stability for one dimensional heat equation on an infinite rod. Further, the paper investigates the stability of heat equation in ?with init...In this paper we apply the Fourier transform to prove the Hyers-Ulam-Rassias stability for one dimensional heat equation on an infinite rod. Further, the paper investigates the stability of heat equation in ?with initial condition, in the sense of Hyers-Ulam-Rassias. We have also used Laplace transform to establish the modified Hyers-Ulam-Rassias stability of initial-boundary value problem for heat equation on a finite rod. Some illustrative examples are given.展开更多
In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve ...In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 〈 α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative.展开更多
文摘This paper is concerned with the stationary plane contact of an insulated rigid punch and a half-space which is elastically anisotropic but thermally conducting. The frictional heat generation inside the contact region due to the sliding of the punch over the half-space surface and the heat radiation outside the contact region are taken into account. With the help of Fourier integral transform, the problem is reduced to a system of two singular integral equations. The equations are solved numerically by using Gauss-Jacobi and trapezoidal-rule quadratures. The effects of anisotropy and thermal effects are shown graphically.
基金NNSF of China (No. 10271050)NSF of Gansu Province, China (ZS021-A25-001-Z)
文摘In this paper we consider a non-standard inverse heat conduction problem for determining surface heat flux from an interior observation which appears in some applied subjects. This problem is ill-posed in the sense that the solution (if it exists)does not depend continuously on the data. A Fourier method is applied to formulate a regularized approximation solution, and some sharp error estimates are also given.
文摘In this paper we apply the Fourier transform to prove the Hyers-Ulam-Rassias stability for one dimensional heat equation on an infinite rod. Further, the paper investigates the stability of heat equation in ?with initial condition, in the sense of Hyers-Ulam-Rassias. We have also used Laplace transform to establish the modified Hyers-Ulam-Rassias stability of initial-boundary value problem for heat equation on a finite rod. Some illustrative examples are given.
基金supported by the National Natural Science Foundation of China(11072134 and 11102102)
文摘In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 〈 α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative.
