  We prove the existence and uniqueness of a traveling front and of its speed
for the homogeneous heat equation in the half-plane with a Neumann boundary
reaction term of non-balanced bistable type or of combustion type. We also
establish the monotonicity of the front and, in the bistable case, its behavior
at infinity. In contrast with the classical bistable interior reaction model,
its behavior at the side of the invading state is of power type, while at the
side of the invaded state its decay is exponential. These decay results rely on
the construction of a family of explicit bistable traveling fronts. Our
existence results are obtained via a variational method, while the uniqueness
of the speed and of the front rely on a comparison principle and the sliding
method.
