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

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  • 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.
    Mathematics Subject Classification: 34B40, 35L70.


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