Nodal properties of solutions of parabolic equations (Q803383)

We review some known facts about the zero set of a solution of a scalar parabolic equation \(u_ t=a(x,t)u_{xx}+b(x,t)u_ x+c(x,t)u\), \(x_ 0<x<x_ 1\), \(0<t<T.\) In particular, we discuss some applications to spectral theory, the dynamics of nonlinear diffusion equations, and the geometric heat equation for plane curves.