American Institute of Mathematical Sciences

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March  2003, 9(2): 399-412. doi: 10.3934/dcds.2003.9.399

Kernel sections for damped non-autonomous wave equations with critical exponent

Shengfan Zhou 1, and  Linshan Wang 2,

1. 

Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234, China
2. 

Department of Mathematics, Qingdao Ocean University, Qingdao, 266000, China

Received  June 2001 Revised  March 2002 Published  December 2002

We prove the existence of kernel sections for the process generated by a damped non-autonomous wave equation when there is nonlinear damping and the nonlinearity has a critically growing exponent. We show uniform boundedness of the Hausdorff dimension of the kernel sections. Finally, we point out that in the case of autonomous systems with linear damping, the obtained upper bound of the Hausdorff dimension decreases as the damping grows for suitable large damping.
Keywords: kernel section, Hausdorff dimension., process, Wave equation.
Mathematics Subject Classification: 34B40, 35L7.
Citation: Shengfan Zhou, Linshan Wang. Kernel sections for damped non-autonomous wave equations with critical exponent. Discrete & Continuous Dynamical Systems, 2003, 9 (2) : 399-412. doi: 10.3934/dcds.2003.9.399
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