The principal spectrum for linear nonautonomous parabolic PDEs of second order: Space-independent case
Volume 90 / 2001
Colloquium Mathematicum 90 (2001), 95-100
MSC: 35K99, 35P15.
DOI: 10.4064/cm90-1-8
Abstract
We show that the study of the principal spectrum of a linear nonautonomous parabolic PDE of second order $u_t={{\mit \Delta }}u+a(t)u$ on a bounded domain, with the Dirichlet or Neumann boundary conditions, reduces to the investigation of the spectrum of the linear nonautonomous ODE $\dot {v}=a(t)v$.
