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
In this paper,we study the wellness and long time dynamic behavior of the solution of the initial boundary value problem for a class of higher order Kirchhoff equations <img src="Edit_e49f9c34-0a5d-4ef2-828f-b...In this paper,we study the wellness and long time dynamic behavior of the solution of the initial boundary value problem for a class of higher order Kirchhoff equations <img src="Edit_e49f9c34-0a5d-4ef2-828f-ba3f0912bed3.png" alt="" />with strong damping terms. We will properly assume the stress term <i>M(s)</i><span style="position:relative;top:6pt;"><v:shape id="_x0000_i1026" type="#_x0000_t75" o:ole="" style="width:27pt;height:17.25pt;"><v:imagedata src="file:///C:\Users\TEST~1.SCI\AppData\Local\Temp\msohtmlclip1\01\clip_image002.wmz" o:title=""></v:imagedata></v:shape></span> and<span style="letter-spacing:-0.2pt;"> nonlinear term g(u<sub>t</sub>)<span style="position:relative;top:6pt;"><v:shape id="_x0000_i1027" type="#_x0000_t75" o:ole="" style="width:27pt;height:17.25pt;"><v:imagedata src="file:///C:\Users\TEST~1.SCI\AppData\Local\Temp\msohtmlclip1\01\clip_image003.wmz" o:title=""></v:imagedata></v:shape></span>. First, we can prove the existence and uniqueness of the solution of the equation via a prior estimate and Galerkin’s method, then the existence of the family of global attractor is obtained. At last, we can obtain that the Hausdorff dimension and Fractal dimension of the family of global attractor are finite.</span>展开更多
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.
文摘In this paper,we study the wellness and long time dynamic behavior of the solution of the initial boundary value problem for a class of higher order Kirchhoff equations <img src="Edit_e49f9c34-0a5d-4ef2-828f-ba3f0912bed3.png" alt="" />with strong damping terms. We will properly assume the stress term <i>M(s)</i><span style="position:relative;top:6pt;"><v:shape id="_x0000_i1026" type="#_x0000_t75" o:ole="" style="width:27pt;height:17.25pt;"><v:imagedata src="file:///C:\Users\TEST~1.SCI\AppData\Local\Temp\msohtmlclip1\01\clip_image002.wmz" o:title=""></v:imagedata></v:shape></span> and<span style="letter-spacing:-0.2pt;"> nonlinear term g(u<sub>t</sub>)<span style="position:relative;top:6pt;"><v:shape id="_x0000_i1027" type="#_x0000_t75" o:ole="" style="width:27pt;height:17.25pt;"><v:imagedata src="file:///C:\Users\TEST~1.SCI\AppData\Local\Temp\msohtmlclip1\01\clip_image003.wmz" o:title=""></v:imagedata></v:shape></span>. First, we can prove the existence and uniqueness of the solution of the equation via a prior estimate and Galerkin’s method, then the existence of the family of global attractor is obtained. At last, we can obtain that the Hausdorff dimension and Fractal dimension of the family of global attractor are finite.</span>
