15 citations · 30 across the 5 of their papers we have counts for
5 papers
On blowup dynamics in the Keller-Segel model of chemotaxis
S. I. Dejak, D. Egli, P. M. Lushnikov +1
We investigate the (reduced) Keller-Segel equations modeling chemotaxis of bio-organisms. We present a formal derivation and partial rigorous results of the blowup dynamics of solu…
On Spectra of Linearized Operators for Keller-Segel Models of Chemotaxis
S. I. Dejak, P. M. Lushnikov, Yu. N. Ovchinnikov +1
We consider the phenomenon of collapse in the critical Keller-Segel equation (KS) which models chemotactic aggregation of micro-organisms underlying many social activities, e.g. fr…
Blow-up in Nonlinear Heat Equations
S. Dejak, Zhou Gang, I. M. Sigal +1
We study the blow-up problem of one-dimensional nonlinear heat equations. Our result shows that for a certain class of initial conditions, the solutions blow up in finite time and…
Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves
S. I. Dejak, B. L. G. Jonsson
We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficie…
Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom
S. I. Dejak, I. M. Sigal
We study the variable bottom generalized Korteweg-de Vries (bKdV) equation dt u=-dx(dx^2 u+f(u)-b(t,x)u), where f is a nonlinearity and b is a small, bounded and slowly varying fun…