MATH Seminar: “Well-posedness of two dissipative KdV-like equations on a finite interval: a comparison”, Chris Mayo (Bilkent Üniversitesi), 2:00PM November 4, 2026 (EN)

You are cordially invited to the Analysis Seminar organized by the Department of Mathematics.

Speaker: Chris Mayo (Bilkent)

“Well-posedness of two dissipative KdV-like equations on a finite interval: a comparison”

Abstract: The Korteweg-de Vries-Burgers (KdV-B) equation and the Korteweg-de Vries Kuramoto-Sivashinsky (KdV-KS) equation are, respectively, third- and fourth–order nonlinear evolution equations with KdV-type nonlinearities.
Both equations differ from standard Korteweg-de Vries (KdV) by their inclusion of linear dissipation terms; KdV-B contains a second-order term, whereas KdV-KS boasts both second- and fourth-order dissipation. These additions allow KdV-B and KdV-KS to model a wide variety of situations, including those involving shock waves in shallow water, aerated liquid flow, flame fronts, plasmas, and liquid films. Because of the similarities in their structure, a comparison between these two equations is natural.
In this talk, we consider the initial-boundary value problems for KdV-B with negative dispersion and for KdV-KS, both in the context of the finite interval.
More specifically, we establish the local well-posedness of these two problems in the sense of Hadamard (existence and uniqueness of the solution as well as its continuous dependence on the data) for initial data in the Sobolev space Hs and boundary data in suitable Sobolev spaces determined by the regularity of the initial data as well as the respective equation itself. A foundational element of our proofs is the linear solution operator derived through the unified transform of Fokas, from which we extract a wide variety of linear estimates, which we combine with certain nonlinear estimates in order to form a contraction-mapping argument. Along the way, we highlight key similarities and differences between the two problems that arise throughout the process.

Date: November 4, Wednesday
Time: 14:00
Place: SA141