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Full-Text Articles in Physical Sciences and Mathematics
Forced Oscillations Of The Korteweg-De Vries Equation On A Bounded Domain And Their Stability, Muhammad Usman, Bingyu Zhang
Forced Oscillations Of The Korteweg-De Vries Equation On A Bounded Domain And Their Stability, Muhammad Usman, Bingyu Zhang
Mathematics Faculty Publications
It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Kortewg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a bounded domain. Consideration is given to the initial-boundary-value problem
uuxuxxx 0 < x < 1, t > 0, (*)
It is shown …
Coarser Connected Topologies And Non-Normality Points, Lynne Yengulalp
Coarser Connected Topologies And Non-Normality Points, Lynne Yengulalp
Mathematics Faculty Publications
We investigate two topics, coarser connected topologies and non-normality points. The motivating question in the first topic is:
Question 0.0.1. When does a space have a coarser connected topology with a nice topological property? We will discuss some results when the property is Hausdorff and prove that if X is a non-compact metric space that has weight at least c, then it has a coarser connected metrizable topology. The second topic is concerned with the following question:
Question 0.0.2. When is a point y ∈ β X\X a non-normality point of β X\X? We will discuss the question in the …