SIAM Journal on Mathematical Analysis· 2026Q1
Well-Posedness and Energy Decay for KdV-B Equations with Time-Dependent Delays
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- Q1SCImago
- 2026year
Short summary
This paper establishes global existence and exponential decay for the Korteweg–de Vries–Burgers equation with a time-dependent delay feedback, achieving exponential stability without smallness conditions on the delay when the delay function has higher regularity.
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Key points
- Establishes global existence of solutions for the KdV-B equation with time-dependent delay feedback.
- Derives exponential decay estimates for solutions in both continuous and regularly-behaved delay settings.
- Achieves exponential stability without smallness conditions on the delay size when the delay function has higher regularity.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract. In this paper, we study the well-posedness and exponential stability of the generalized Korteweg–de Vries–Burgers equation incorporating a damping term and a time-dependent delay feedback. The delay function is examined under two distinct frameworks: one in which it is assumed to be merely continuous, and another in which it satisfies additional regularity conditions, while remaining bounded in both cases. Under suitable assumptions on the delay feedback, we establish the global existence of solutions. Moreover, we derive exponential decay estimates in both delay settings. Notably, in the case where the delay function exhibits higher regularity, exponential stability is obtained without requiring any smallness conditions on the time delay size.
The authors' abstract, as published at the source. SIAM Journal on Mathematical Analysis, 2026 · DOI ↗
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Field: Control and Systems Engineering
Control and Systems EngineeringEngineering