Well-posedness and Stabiliy result of Petrovsky equation with a nonlinear strong damping and delay term

Ahmed Chahtou; Mama Abdelli; Akram Ben Aissa

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arXiv · 2011.06503

Well-posedness and Stabiliy result of Petrovsky equation with a nonlinear strong damping and delay term

Ahmed Chahtou·Mama Abdelli·Akram Ben Aissa

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Abstract

In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation \begin{align*} u_{tt} + \Delta^{2} u -\mu_1g_1( \Delta( u_t(x,t))) -\mu_2g_2( \Delta (u_t(x,t-\tau))) =0. \end{align*} We prove the existence of global solutions in suitable Sobolev spaces by using the energy method combined with Faedo-Galarkin method under condition on the weight of the delay term in the feedback and the weight of the term without delay. Furthermore, we study general stability estimates by using some properties of convex functions.

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Ahmed Chahtou, Mama Abdelli, Akram Ben Aissa. 2020-11-12. Well-posedness and Stabiliy result of Petrovsky equation with a nonlinear strong damping and delay term. https://arxiv.org/abs/2011.06503

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