Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the curvature...Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coefficients. In particular, some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given.展开更多
This paper considers the existence of global smooth solutions of semilinear schrSdinger equation with a boundary feedback on 2-dimensional Riemannian manifolds when initial data are small. The authors show that the ex...This paper considers the existence of global smooth solutions of semilinear schrSdinger equation with a boundary feedback on 2-dimensional Riemannian manifolds when initial data are small. The authors show that the existence of global solutions depends not only on the boundary feedback, but also on a Riemannian metric, given by the coefficient of the principle part and the original metric of the manifold. In particular, the authers prove that the energy of the system decays exponentially.展开更多
The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach.
基金supported by the National Natural Science Foundation of China (Nos.60225003,60821091,10831007,60774025)KJCX3-SYW-S01
文摘Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coefficients. In particular, some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given.
基金supported by the National Science Foundation of China under Grants Nos. 60225003, 60334040, 60221301, 60774025, and 10831007Chinese Academy of Sciences under Grant No KJCX3-SYW-S01
文摘This paper considers the existence of global smooth solutions of semilinear schrSdinger equation with a boundary feedback on 2-dimensional Riemannian manifolds when initial data are small. The authors show that the existence of global solutions depends not only on the boundary feedback, but also on a Riemannian metric, given by the coefficient of the principle part and the original metric of the manifold. In particular, the authers prove that the energy of the system decays exponentially.
基金supported by the National Science Foundation of China under Grant Nos.60225003,60334040,60221301,60774025,10831007,61104129,11171195the Excellent PhD Adviser Program of Beijing under Grant No.YB20098000101
文摘The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach.
