Title:Nonlinear stability of traveling waves to Burgers equation with fast diffusion
Speaker:李敬宇 （Northeast Normal University）
Abstract: In this talk we propose the framework to study Burgers equation featuring fast diffusion in form of u_t+f(u)_x = g(u)_{xx}. Here g(u)=\frac{u^m}{m} with 0<m<1 the fast diffusion, m<0 the ultra-fast diffusion, and g(u)= \ln u the logarithmic fast diffusion. In each case, the solution possesses a singularity when u=0 hence bringing technical challenges. Our main purpose is to investigate the asymptotic stability of traveling waves, particularly those vanishing at the far field x=+\infty. To overcome the singularity, we introduce some weight functions and show the nonlinear stability of traveling waves through the weighted energy method.
Time:11.12（Tuesday），14:30-16:30
Location: #Tencent meeting 193-857-987 Password：161616
