The global attractors and dimensions estimation for the Kirchho type wave equations with nonlinear strongly damped terms | Zendy

Chengfei Ai | Zendy; Huixian Zhu | Zendy; Guoguang Lin | Zendy

Open Access

The global attractors and dimensions estimation for the Kirchho type wave equations with nonlinear strongly damped terms

Author(s) -

Chengfei Ai,

Huixian Zhu,

Guoguang Lin

Publication year - 2016

Publication title -

journal of advances in mathematics

Language(s) - English

Resource type - Journals

ISSN - 2347-1921

DOI - 10.24297/jam.v12i3.492

Subject(s) - mathematics , attractor , uniqueness , type (biology) , galerkin method , nonlinear system , mathematical analysis , a priori and a posteriori , fractal , wave equation , class (philosophy) , biology , ecology , philosophy , physics , epistemology , quantum mechanics , artificial intelligence , computer science

This paper studies the long time behavior of the solution to the initial boundaryvalue problems for a class of strongly damped Kirchho type wave equations:utt "1ut + j ut jp1 ut + j u jq1 u (kruk2)u = f(x):Firstly, we prove the existence and uniqueness of the solution by priori estimate and the Galerkin method. Then we obtain to the existence of the global attractor. Finally, we consider that the estimation of the upper bounds of Hausdor and fractal dimensionsfor the global attractor is obtained.

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