The minimal positive solutions of the heat equation on X × (-∞, T) are determined for X a homogeneous Riemannian space. A simple proof of uniqueness for the positive Cauchy problem on a homogeneous ...

We give a new proof of the fact that the solutions of the stochastic heat equation, started with nonnegative initial conditions, are strictly positive at positive times. The proof uses concentration ...

The study of controllability for parabolic and heat equations focuses on the capability to steer the temporal evolution of diffusion-dominated processes towards desired states. Central to this field ...