Applied Math/PDE Seminar: Hiroshi Takeda (Fukuoka Inst. of Tech.), 'Large time behavior of global solutions of the semilinear damped beam equation'

Event Date: 

Friday, March 21, 2014 -
3:00pm to 4:00pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Carlos Garcia-Cervera

Email: cgarcia@math.ucsb.edu

Phone: 18055638873

In this talk, we consider the existence of the global solution and its asymptotic profile for the Cauchy problem for the nonlinear damped beam equation. We show that the equation admits a unique global solution with small slowly decaying data. Moreover we show that the solution can be approximated by the solution of the linear heat equation with suitable data. The proof is based upon the estimates for the evolution operator of the linearized equation in the homogeneous Sobolev space.