We study the Fisher-KPP equation with a free boundary governed by a one-phase Stefan condition. Such a problem arises in the modeling of the propagation of a new or invasive species, with the free boundary representing the propagation front. In one space dimension and the radially symmetric case in higher space dimensions this problem was studied by some authors. In both cases a spreading-vanis...

We prove the existence and uniqueness, local in time, of a solution for a one-phase Stefan problem of a non-classical heat equation for a semiinfinite material with temperature boundary condition at the fixed face. We use the Friedman-Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations.

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell’s equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.