Blow-up solutions in semilinear heat equations refer to phenomena where solutions become unbounded in finite time, an occurrence that has far‐reaching implications for the study of nonlinear partial ...

The Annals of Applied Probability, Vol. 28, No. 3 (June 2018), pp. 1943-1976 (34 pages) The initial-boundary value problem for the heat equation is solved by using an algorithm based on a random walk ...

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 ...

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 ...