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Large data solutions for semilinear higher order equations

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  • In this paper we study local and global in time existence for a class of nonlinear evolution equations having order eventually greater than 2 and not integer. The linear operator has an homogeneous damping term; the nonlinearity is of polynomial type without derivatives:

    $ u_{tt}+ (-\Delta)^{2\theta}u+2\mu(-\Delta)^\theta u_t + |u|^{p-1}u = 0, \quad t\geq0, \ x\in {\mathbb{R}}^n, $

    with $ \mu>0 $, $ \theta>0 $. Since we are treating an absorbing nonlinear term, large data solutions can be considered.

    Mathematics Subject Classification: Primary: 35L71, 35L82, 35B40.


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