Instability of solutions of a semilinear heat equation with a neumann boundary condition
A semilinear heat equation u t = u x x + eup, 0 0, subject to u x (0,t) = 0,u x (1,t) = -u - q (1,t), q > 0 is studied. The set of stationary states is characterized, their instability is analyzed, and the large time behavior of positive solutions is discussed.