| Abstract: |
| In this talk, we analyze the decay properties of a class of higher-order nonlinear dispersive systems with time delay, extending classical models of KdV--Burgers type to a more general setting. The equations under consideration incorporate both dispersive and dissipative effects, together with a delayed feedback term acting on the dynamics.
We show that the presence of delay can still lead to exponential decay of solutions under suitable structural conditions on the feedback coefficients. In particular, stabilization is achieved without imposing sign restrictions on the instantaneous damping term, highlighting the effective role of the delayed mechanism.
In addition, we discuss the behavior of the system in the absence of delay and establish general decay results in Sobolev spaces, covering a broad range of regularity. The results provide a unified qualitative framework for understanding the interplay between dispersion, dissipation, and memory effects in higher-order evolution equations posed on unbounded domains. |
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