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<p>We study a one-dimensional fourth-order Schrödinger-type equation with a fractional phase parameter that interpolates between diffusive and conservative dynamics. Our analysis provides a unified description of the linear and semilinear flows, highlighting decay and dissipation mechanisms and their dependence on the phase. We further address robustness with respect to the fractional parameter by establishing local-in-time stability and by justifying convergence to the endpoint models as the parameter approaches the heat-type and Schrödinger-type limits.</p>

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DECAY AND STABILITY FOR A CLASS OF FOURTH-ORDER SCHRÖDINGER EQUATIONS

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Nguyen Duc Phuong

摘要

We study a one-dimensional fourth-order Schrödinger-type equation with a fractional phase parameter that interpolates between diffusive and conservative dynamics. Our analysis provides a unified description of the linear and semilinear flows, highlighting decay and dissipation mechanisms and their dependence on the phase. We further address robustness with respect to the fractional parameter by establishing local-in-time stability and by justifying convergence to the endpoint models as the parameter approaches the heat-type and Schrödinger-type limits.