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 ...

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 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 examine a heat problem in 1D. Assume that a rod with given temperature distribution u_0(x) is cooled to temperature 0 on the exteriors at 0 and pi. Assume that u(x,t) for the Temperature at point x ...