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Longtime dynamics for an elastic waveguide model

Pages: 797 - 806, Issue special, November 2013

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Zhijian Yang - Department of Mathematics, Zhengzhou University, No.100, Science Road, Zhengzhou 450001, China (email)
Ke Li - Department of Mathematics, Zhengzhou University, No.100, Science Road, Zhengzhou 450001, China (email)

Abstract: The paper studies the longtime dynamics for a nonlinear wave equation arising in elastic waveguide model´╝Ü $u_{tt}- \Delta u-\Delta u_{tt}+\Delta^2 u- \Delta u_t -\Delta g(u)=f(x)$. It proves that the equation possesses in trajectory phase space a global trajectory attractor $\mathcal{A}^{tr}$ and the full trajectory of the equation in $\mathcal{A}^{tr}$ is of backward regularity provided that the growth exponent of nonlinearity $g(u)$ is supercritical.

Keywords:  Nonlinear wave equation, global solution, longtime dynamics, trajectory attractor, backward regularity.
Mathematics Subject Classification:  Primary: 35B40, 35B41; Secondary: 35G31, 35L35, 37L30.

Received: September 2012; Published: November 2013.

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