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ACMD Seminar: Analysis of the modified Burgers equation on the half line

John Holmes
Mathematics Department, Ohio State University

Tuesday, September 20, 2022, 3:00-4:00 EDT (1:00-2:00 MDT)

A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.

Abstract: Physical phenomenon modeled by partial differential equations (PDEs) often have a natural formulation on domains with a boundary. A novel approach to studying PDEs on the half line and interval was introduced recently by Fokas. Fokas’ method generalizes the Fourier transform and allows one to solve the initial-boundary value problem (IBVP) for linear PDEs explicitly on the half line and interval. Analogous to the Fourier transform on the whole line, this approach also allows one to define mild solutions to nonlinear PDEs on the half line as fixed points of a contractive operator. In this talk we will explore this approach using the modified Burgers equation ut + u2ux = uxx as our main vehicle. We will also prove the well-posedness for the corresponding IBVP in spaces of low regularity.

Bio: John Holmes received his PhD from the University of Notre Dame in 2015. He then worked at The Ohio State University as a Ross Assistant Professor and the Charles Saltzer Postdoctoral Researcher before accepting a tenure track position at Wake Forest University. He returned to The Ohio State University this fall as a tenure track assistant professor.

Host: Rob Dejaco

Note: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

Note: Visitors from outside NIST must contact Lochi Orr (301) 975-3800; at least 24 hours in advance.

Created August 29, 2022, Updated September 21, 2022