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

Shengfan Zhou; Linshan Wang

doi:10.3934/dcds.2003.9.399

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2003, Volume 9, Issue 2: 399-412. Doi: 10.3934/dcds.2003.9.399

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

Shengfan Zhou^1, and
Linshan Wang²

1.
Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234
2.
Department of Mathematics, Qingdao Ocean University, Qingdao, 266000

Received: June 2001

Revised: March 2002

Published: March 2003

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Abstract

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.

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Mathematics Subject Classification: 34B40, 35L70.

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