This paper is concerned with the initial boundary value problem for a viscoelastic model with relaxation. Under the only assumption that the C^0-norm of the initial data is small, without smallness hypothesis for the ...This paper is concerned with the initial boundary value problem for a viscoelastic model with relaxation. Under the only assumption that the C^0-norm of the initial data is small, without smallness hypothesis for the C^1-norm, the existence of the global smooth solution to the corresponding initial boundary value problem is proved. The analysis is based on some a priori estimates obtained by the 'maximum principle' of first-order quasilinear hyperbolic system.展开更多
This paper considers the asymptotic behavior of solutions to the system of onedimensional viscoelastic model with damping and prove that the corresponding solutions time-asymptotically behave like nonlinear diffusion ...This paper considers the asymptotic behavior of solutions to the system of onedimensional viscoelastic model with damping and prove that the corresponding solutions time-asymptotically behave like nonlinear diffusion wave as in [4,11]. In addition, It is also shown that the system of one-dimensional viscoelastic model with damping is a viscosity approximation of a hyperbolic conservation laws with damping.展开更多
In this paper, Under the assumption that the relaxation time ε is sufficiently small, we prove the existence of the global smooth solution to the Cauchy problem for the Jin-Xin model without any smallness assumption ...In this paper, Under the assumption that the relaxation time ε is sufficiently small, we prove the existence of the global smooth solution to the Cauchy problem for the Jin-Xin model without any smallness assumption for the initial data.The analysis is based on some a priori estimates which are obtained by the method of characteristic and the maximum principle of first-order quasilinear hyperbolic system.展开更多
We investigate the asymptotic behavior of solutions of the initial-boundaryvalue problem for the generalized BBM-Burgers equation u_t + f(u)_x = u_(xx) + u_(xxt) on the halfline with the conditions u(0, t) = u_–, u(...We investigate the asymptotic behavior of solutions of the initial-boundaryvalue problem for the generalized BBM-Burgers equation u_t + f(u)_x = u_(xx) + u_(xxt) on the halfline with the conditions u(0, t) = u_–, u(∞, t) = u + and u_– 【 u_+, where the correspondingCauchy problem admits the rarefaction wave as an asymptotic states. In the present problem, becauseof the Dirichlet boundary, the asymptotic states are divided into five cases depending on the signsof the characteristic speeds f(u_±) of boundary state u_– = u(0) and the far fields states u_+ =u(∞). In all cases both global existence of the solution and asymptotic behavior are shown underthe smallness conditions.展开更多
An excellent introduction to the topic of poset matroids is due to M.Barnabei, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rankaxioms for poset matroids. In this paper, we stud...An excellent introduction to the topic of poset matroids is due to M.Barnabei, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rankaxioms for poset matroids. In this paper, we study the special integral function f and obtain a newclass of poset matroids from the old ones, and then we generalize this result according to theproperties of f. Almost all of these results can be regarded as the application of global rankaxioms for poset matroids. The main results in our paper have, indeed, investigated the restrictionof the basis of the poset matroid, and we give them the corresponding geometric interpretation.展开更多
基金The research was supported by the Natural Science Foundation of China(10171037)the National Key Program for Basic Research of China(2002CCA03700)respectivelyThe first author was supported by south central university for Nationalities Nature Science F
文摘This paper is concerned with the initial boundary value problem for a viscoelastic model with relaxation. Under the only assumption that the C^0-norm of the initial data is small, without smallness hypothesis for the C^1-norm, the existence of the global smooth solution to the corresponding initial boundary value problem is proved. The analysis is based on some a priori estimates obtained by the 'maximum principle' of first-order quasilinear hyperbolic system.
文摘This paper considers the asymptotic behavior of solutions to the system of onedimensional viscoelastic model with damping and prove that the corresponding solutions time-asymptotically behave like nonlinear diffusion wave as in [4,11]. In addition, It is also shown that the system of one-dimensional viscoelastic model with damping is a viscosity approximation of a hyperbolic conservation laws with damping.
文摘In this paper, Under the assumption that the relaxation time ε is sufficiently small, we prove the existence of the global smooth solution to the Cauchy problem for the Jin-Xin model without any smallness assumption for the initial data.The analysis is based on some a priori estimates which are obtained by the method of characteristic and the maximum principle of first-order quasilinear hyperbolic system.
基金Supported by the National Natural Science Foundation of China (No.10171037, No. 10401012)
文摘We investigate the asymptotic behavior of solutions of the initial-boundaryvalue problem for the generalized BBM-Burgers equation u_t + f(u)_x = u_(xx) + u_(xxt) on the halfline with the conditions u(0, t) = u_–, u(∞, t) = u + and u_– 【 u_+, where the correspondingCauchy problem admits the rarefaction wave as an asymptotic states. In the present problem, becauseof the Dirichlet boundary, the asymptotic states are divided into five cases depending on the signsof the characteristic speeds f(u_±) of boundary state u_– = u(0) and the far fields states u_+ =u(∞). In all cases both global existence of the solution and asymptotic behavior are shown underthe smallness conditions.
基金Supported partially by the National Natural Science Foundation of China(Grant No.10371048)
文摘An excellent introduction to the topic of poset matroids is due to M.Barnabei, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rankaxioms for poset matroids. In this paper, we study the special integral function f and obtain a newclass of poset matroids from the old ones, and then we generalize this result according to theproperties of f. Almost all of these results can be regarded as the application of global rankaxioms for poset matroids. The main results in our paper have, indeed, investigated the restrictionof the basis of the poset matroid, and we give them the corresponding geometric interpretation.
