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Fourth-Order Damped Wave Equation with Exponential Growth Nonlinearity

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Abstract

The initial boundary value problem for a damped fourth-order wave equation with exponential growth nonlinearity is investigated in four space dimensions. In the defocusing case, global well-posedness, scattering and exponential decay are established. In the focusing sign, existence of ground state, instability of standing waves and blow-up results are obtained.

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Authors and Affiliations

  1. Faculty of Science of Tunis, University of Tunis El Manar, LR03ES04 partial differential Equations and applications, 2092, Tunis, Tunisia

    Tarek Saanouni

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  1. Tarek Saanouni
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Correspondence to Tarek Saanouni.

Additional information

Communicated by Nader Masmoudi.

T. Saanouni is grateful to the Laboratory of PDE and Applications at the Faculty of Sciences of Tunis.

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Saanouni, T. Fourth-Order Damped Wave Equation with Exponential Growth Nonlinearity. Ann. Henri Poincaré 18, 345–374 (2017). https://doi.org/10.1007/s00023-016-0512-7

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  • DOI: https://doi.org/10.1007/s00023-016-0512-7

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