Ohio State is in the process of revising websites and program materials to accurately reflect compliance with the law. While this work occurs, language referencing protected class status or other activities prohibited by Ohio Senate Bill 1 may still appear in some places. However, all programs and activities are being administered in compliance with federal and state law.

Singular radial solutions for super-critical Keller-Segel and Lin-Ni-Takagi equation

PDE Seminar
October 4, 2021
10:20 am - 11:20 am
MW154 and Zoom

Title:  Singular radial solutions for super-critical Keller-Segel and Lin-Ni-Takagi equation

Speaker:  Juraj Foldes (University of Virginia)

Speaker's URL:  https://uva.theopenscholar.com/juraj-foldes/

Abstract:  We will discuss singular radially symmetric solution of the stationary Keller-Segel and Lin-Ni-Takagi equation, that is, an elliptic equation with exponential or power nonlinearity, which is super-critical in dimension bigger than 2. The solutions are unbounded at the origin, and we show that they describe the asymptotics of bifurcation branches of regular solutions. In particular, we will prove that for any ball and any positive k, there is a singular solution that satisfies Neumann boundary condition and oscillates at least k times around the constant equilibrium. Moreover, we will show that in dimension 3 ≤ N ≤ 9 there are regular solutions satisfying Neumann boundary conditions that are close to singular ones. Hence, it follows that there exist regular solutions on any ball with arbitrarily fast oscillations. This is a joint work with Denis Bonheure (Université libre de Bruxelles) and Jean-Baptiste Casteras (Universidade de Lisboa).

Zoom ID 935 1740 8580 Password: 314159

 

Events Filters:

Seminar - PDE