In this paper, we study the long-time behavior of the solution of the initial boundary value problem of the coupled Kirchhoff equations. Based on the relevant assumptions, the equivalent norm on E<sub>k</sub&...In this paper, we study the long-time behavior of the solution of the initial boundary value problem of the coupled Kirchhoff equations. Based on the relevant assumptions, the equivalent norm on E<sub>k</sub> is obtained by using the Hadamard graph transformation method, and the Lipschitz constant l<sub>F</sub><sub> </sub>of F is further estimated. Finally, a family of inertial manifolds satisfying the spectral interval condition is obtained.展开更多
In this paper, we study the inertial manifolds for a class of asymmetrically coupled generalized Higher-order Kirchhoff equations. Under appropriate assumptions, we firstly exist Hadamard’s graph transformation metho...In this paper, we study the inertial manifolds for a class of asymmetrically coupled generalized Higher-order Kirchhoff equations. Under appropriate assumptions, we firstly exist Hadamard’s graph transformation method to structure a graph norm of a Lipschitz continuous function, then we prove the existence of a family of inertial manifolds by showing that the spectral gap condition is true.展开更多
文摘In this paper, we study the long-time behavior of the solution of the initial boundary value problem of the coupled Kirchhoff equations. Based on the relevant assumptions, the equivalent norm on E<sub>k</sub> is obtained by using the Hadamard graph transformation method, and the Lipschitz constant l<sub>F</sub><sub> </sub>of F is further estimated. Finally, a family of inertial manifolds satisfying the spectral interval condition is obtained.
文摘In this paper, we study the inertial manifolds for a class of asymmetrically coupled generalized Higher-order Kirchhoff equations. Under appropriate assumptions, we firstly exist Hadamard’s graph transformation method to structure a graph norm of a Lipschitz continuous function, then we prove the existence of a family of inertial manifolds by showing that the spectral gap condition is true.
