Display Abstract

Title Convergence to Steady State for Degenerate Parabolic Equations

Name Shaohua Chen
Country Canada
Email george_chen@cbu.ca
Co-Author(s) Xu Runzhang
Submit Time 2014-02-21 11:08:08
Special Session 37: Global or/and blowup solutions for nonlinear evolution equations and their applications
In this talk, we first discuss large time behavior of the homogeneous Dirichlet problem to the degenerate parabolic equation $u_t = g(u) \D u + f(u)$ in a bounded domain $\Omega \subset R^n$ with smooth boundary $\partial \Omega$. Under suitable conditions on $f(u)$ and $g(u)$, we show that all solutions will converge to the steady state exponentially. Next, we study the degenerate parabolic system $u_t = u \D u + u(a_1-b_1 u +c_1 v)$ and $v_t = v \D v + v(a_2+b_2 u -c_2 v)$ with the same boundary condition. We show that any positive solutions converge to a unique steady state exponentially if the coefficients satisfy some conditions.