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

Zhou, Shengfan

doi:10.1090/qam/2019621

Author: Shengfan Zhou
Journal: Quart. Appl. Math. 61 (2003), 731-757
MSC: Primary 37L30; Secondary 35L70, 35R10
DOI: https://doi.org/10.1090/qam/2019621
MathSciNet review: MR2019621
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Abstract: We prove the existence of kernel sections for the process generated by a non-autonomous wave equation with linear memory when there is nonlinear damping and the nonlinearity has a critically growing exponent; we also obtain a more precise estimate of upper bound of the Hausdorff dimension of the kernel sections. And 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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