In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigrou...In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space <em>E</em><sub>0</sub> to <em>E<sub>k</sub></em>, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition.展开更多
In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup ...In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup associated with the initial boundary value problem are proved, and the existence of a family of exponential attractors is obtained. Then, by constructing the corresponding graph norm, the condition of a spectral interval is established when N is sufficiently large. Finally, the existence of the family of inertial manifolds is obtained.展开更多
The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian sta...The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian states with various non-classical properties.In this paper,the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field.The density operator of the new light field,its entanglement property and photon number distribution are analyzed.We also note that tracing a three-mode pure state can yield this new light field.These methods represent a theoretical approach to investigating new density operators of light fields.展开更多
文摘In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space <em>E</em><sub>0</sub> to <em>E<sub>k</sub></em>, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition.
文摘In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup associated with the initial boundary value problem are proved, and the existence of a family of exponential attractors is obtained. Then, by constructing the corresponding graph norm, the condition of a spectral interval is established when N is sufficiently large. Finally, the existence of the family of inertial manifolds is obtained.
基金Project supported by the National Natural Science Foundation of China(Grant No.11775208)the Foundation for Young Talents in College of Anhui Province,China(Grant Nos.gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant Nos.KJ2020A0638 and 2022AH051586)。
文摘The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian states with various non-classical properties.In this paper,the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field.The density operator of the new light field,its entanglement property and photon number distribution are analyzed.We also note that tracing a three-mode pure state can yield this new light field.These methods represent a theoretical approach to investigating new density operators of light fields.
