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 ...

Quarterly of Applied Mathematics, Vol. 68, No. 1 (March 2010), pp. 61-71 (11 pages) We address the problem of describing solutions of the nonlinear Schrödinger equation on a compact surface in the ...

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 ...