Events for 04/20/2021 from all calendars

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Federico Pasqualotto, UC Berkeley

Title: Gradient blow-up for dispersive and dissipative perturbations of the Burgers equation

Abstract: In this talk, I will discuss a construction of ”shock forming” solutions to a class of dispersive and dissipative perturbations of the Burgers equation. This class includes the fractional KdV equation with dispersive term of order α ∈ [0,1), the Whitham equation arising in water waves, and the fractal Burgers equation with dissipation term of order β ∈ [0,1). Our result seems to be the first construction of a shock forming solution for fractional KdV in the range α ∈ [2/3,1). We construct blow-up solutions by a self-similar approach, treating the dispersive term as perturbative. The blow up constructed is stable for α < 2/3. However, for α ≥ 2/3, the solution is constructed by perturbing an underlying unstable self-similar Burgers profile. This is joint work with Sung-Jin Oh (UC Berkeley).