Abstract
We investigate the global well-posedness and the global attractors of the solutions for the Higher-order Kirchhoff-type wave equation with nonlinear strongly damping: . For strong nonlinear damping σ and ?, we make assumptions (H1) - (H4). Under of the proper assume, the main results are existence and uniqueness of the solution in proved by Galerkin method, and deal with the global attractors.
Highlights
IntroductionWe consider the following Higher-order Kirchhoff-type equation:. where m > 1 is an integer constant, and Ω is a bounded domain of Rn , with a smooth dirichlet boundary ∂Ω and initial value
We consider the following Higher-order Kirchhoff-type equation:( ) ( ) utt + σ ∇mu 2 (−∆)m ut + φ ∇mu 2= (−∆)m u f ( x),( x,t ) ∈ Ω ×[0, +∞), (1.1) u ( x,=t ) 0, ∂∂νi=ui 0=, i m −1, x ∈ ∂Ω, t (0, +∞) (1.2)
We study the global attractor of the solution for Higher-order Kirchhofftype equations
Summary
We consider the following Higher-order Kirchhoff-type equation:. where m > 1 is an integer constant, and Ω is a bounded domain of Rn , with a smooth dirichlet boundary ∂Ω and initial value. ( ) ( ) tractors in natural energy sp= ace H H1 RN × L2 RN in critical nonlinearity case On this basis, they investigated the global well-posedness and the longtime dynamics of the Kirchhoff equation with fractional damping and supertical nonlinearity [3]:. On the basis of Igor Chueshov, we investigate the global attractor of the higher-order Kirchhoff-type Equation (1.1) with strong nonlinear damping. Such problems have ( ) been studied by many authors, but σ ∇mu 2 is a definite constant and even ( ) σ ∇mu 2 = 0. At last, according to define, we obtain to the existence of the global attractor
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Modern Nonlinear Theory and Application
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
