You are cordially invited to the seminars organized by the Department of Mathematics.<\/p>\n
Speaker: Chris Mayo (U. of Kansas)<\/p>\n
“Analysis of nonhomogeneous initial-boundary value problems for nonlinear evolution PDEs”<\/p>\n
Abstract: One of the most important properties of a partial differential equation (PDE) is well-posedness, meaning the existence of a unique solution that depends continuously on the associated data. Historically, well-posedness was primarily considered in the setting of the initial value problem (IVP), where the spatial domain is $\\mathbb R^n$ or $\\mathbb T^n$. However, many phenomena and applications from fields such as optics, water waves, and control theory occur in domains with a boundary and are thus naturally modeled by initial-boundary value problems (IBVPs). The well-posedness of IBVPs is far less studied due to several reasons, including the lack of Fourier transform in that setting.<\/p>\n
In this talk, we present the rigorous local well-posedness theory for such IBVPs in the case of two different types of nonlinear evolution PDEs \u2014 a higher-order nonlinear Schr”odinger (HNLS) equation and a generalized Korteweg-de Vries\/Kuramoto-Sivashinsky (KdV-KS) equation \u2014 supplemented with nonzero boundary conditions. The techniques we develop allow us to handle PDEs set on the half-line or the finite interval, having multiple linear terms, and exhibiting dispersive and\/or dissipative behavior, all while working within high, low, and negative regularity settings. A key element of our analysis is the linear solution operator derived through the unified transform of Fokas, from which we may extract a wide variety of linear estimates, which when combined with additional nonlinear estimates, form the backbone of our proofs.<\/p>\n
Date: November 26, Wednesday
\nTime: 19:00 (Turkey)
\nPlace: Zoom<\/p>\n
To request the event link, please send a message to turker.ozsari@bilkent.edu.tr<\/p>\n","protected":false},"excerpt":{"rendered":"
You are cordially invited to the seminars organized by the Department of Mathematics. Speaker: Chris Mayo (U. of Kansas) “Analysis of nonhomogeneous initial-boundary value problems for nonlinear evolution PDEs” Abstract: One of the most important properties of a partial differential equation (PDE) is well-posedness, meaning the existence of a unique [\u2026] <\/p>\n